dataesr/scientific-paragraphs-categorization huggingface dataset:
Shortcomings and future questions Given the complexity of recompiling complex software libraries, pre-processing was not perturbed in these experiments as the instrumentation of the canonical workflow used in diffusion image processing would have added considerable technical complexity and computational overhead to the large set of experiments performed here; similarly, this complexity along with the added layer of difficulty in comparing instrumentations meant that only algorithms within a single library were tested. Other work has shown that linear registration, a core piece of many elements of pre-processing such as motion correction and alignment, is sensitive to minor perturbations  [21]. It is likely that the instabilities across the entire processing workflow would be compounded with one another, resulting in even greater variability.
While the analyses performed in this paper evaluated a single dataset and set of pipelines, extending this work to other modalities and analyses, alongside the detection of local sources of instability within pipelines, is of interest for future projects. This paper does not explore methodological flexibility or compare this to numerical instability. Recently, the nearly boundless space of analysis pipelines and their impact on outcomes in brain imaging has been clearly demonstrated  [17]. The approach taken in these studies complement one another and explore instability at the opposite ends of the spectrum, with human variability in the construction of an analysis workflow on one end and the unavoidable error implicit in the digital representation of data on the other. It is of extreme interest to combine these approaches and explore the interaction of these scientific degrees of freedom with effects from software implementations, libraries, and parametric choices.
Dataset The Nathan Kline Institute Rockland Sample (NKI-RS)  [27]  dataset contains high-fidelity imaging and phenotypic data from over 1,000 individuals spread across the lifespan. A subset of this dataset was chosen for each experiment to both match sample sizes presented in the original analyses and to minimize the computational burden of performing MCA. The selected subset comprises 100 individuals ranging in age from 6-79 with a mean of 36. 8 (original: 6-81, mean 37. 8), 60% female (original: 60%), with 52% having a BMI over 25 (original: 54%). Each selected individual had at least a single session of both structural T1-weighted (MPRAGE) and diffusion-weighted (DWI) MR imaging data. DWI data was acquired with 137 diffusion directions in a single shell; more information regarding the acquisition of this dataset can be found in the NKI-RS data release  [27].
In addition to the 100 sessions mentioned above, 25 individuals had a second session to be used in a test-retest analysis. Two additional copies of the data for these individuals were generated, including only the odd or even diffusion directions (64 + 9 B0 volumes = 73 in either case) such that the acquired data was evenly represented across both portions, and each subsample represented a realistic complete acquisition. This allowed for an extra level of stability evaluation to be performed between the levels of MCA and session-level variation. In total, the dataset is composed of 100 subsampled sessions of data originating from 50 acquisitions and 25 individuals for in depth stability analysis, and an additional 100 sessions of full-resolution data from 100 individuals for subsequent analyses.
Processing The dataset was preprocessed using a standard FSL  [37]  workflow consisting of eddy-current correction and alignment. The MNI152 atlas  [38]  was aligned to each session of data via the structural images, and the resulting transformation was applied to the DKT parcellation  [39]. Subsampling the diffusion data took place after preprocessing was performed on full-resolution sessions, ensuring that an additional confound was not introduced in this process when comparing between downsampled sessions. The preprocessing described here was performed once without MCA, and thus is not being evaluated. Structural connectomes were generated from preprocessed data using two canonical pipelines from Dipy  [28] : deterministic and probabilistic. In the deterministic pipeline, a constant solid angle model was used to estimate tensors at each voxel and streamlines were then generated using the EuDX algorithm  [29].
The former is referred to as Precision Bounding (PB) and the latter is called Random Rounding (RR). Using MCA, the execution of a pipeline may be performed many times to produce a distribution of results. Studying the distribution of these results can then lead to insights on the stability of the instrumented tools or functions. To this end, a complete software stack was instrumented with MCA and is made available on GitHub at https://github. com/verificarlo/ fuzzy. The RR variant of MCA was used for all experiments. As was presented in  [19] , both the degree of instrumentation (i. e. number of affected libraries) and the perturbation mode have an effect on the distribution of observed results. For this work, the RR-MCA was applied across the bulk of the relevant operations (those occurring in BLAS, LAPACK, Python, Cython, and Numpy) and is referred to as dense perturbation.
In this case the bulk of numerical operations were affected by MCA. Conversely, the case in which RR-MCA was applied across the operations in a small subset of operations (those ocurring in Python and Cython) is here referred to as sparse perturbation. In this case, the inputs to operations within the instrumented libraries were perturbed, resulting in less frequent, data-centric perturbations. Alongside the stated theoretical differences, sparse perturbation is considerably less computationally expensive than dense perturbation. All perturbations targeted the least-significant-bit for all data (t = 24 and t = 53 in float32 and float64, respectively  [26] ). Perturbing the least significant bit importantly serves as a perturbation of machine error, and thus is the appropriate precision to be applied globally in complex pipelines.
We carried out one such study and explored the instability of its results with respect to the upstream variability of connectomes characterized in the previous sections. We performed the modeling task with a single sampled connectome per individual and repeated this sampling and modelling 20 times. We report the model performance for each sampling of the dataset and summarize its variance. BMI classification. Structural changes have been linked to obesity in adolescents and adults  [42]. We classified normal-weight and overweight individuals from their structural networks (using for overweight a cutoff of BMI >25  [33] ). We reduced the dimensionality of the connectomes through principal component analysis (PCA), and provided the first N-components to a logistic regression classifier for predicting BMI class membership, similar to methods shown in  [32, 33].
The number of components was selected as the minimum set which explained >90% of the variance when averaged across the training set for each fold within the cross validation of the original graphs; this resulted in a feature of 20 components. We trained the model using k-fold cross validation, with k = 2,5,10, and N (equivalent to leave-one-out; LOO). Data & code provenance. The unprocessed dataset is available through The Consortium of Reliability and Reproducibility (http://fcon_1000. projects. nitrc. org/indi/enhanced/), including both the imaging data as well as phenotypic data which may be obtained upon submission and compliance with a Data Usage Agreement. The connectomes generated through simulations have been bundled and stored permanently (https://doi. org/10. 5281/zenodo. 4041549), and made available through The Canadian Open Neuroscience Platform (https://portal.
conp. ca/search, search term "Kiar"). All software developed for processing or evaluation is publicly available on GitHub at https://github. com/gkpapers/2021ImpactOfInstability. Experiments were launched using Boutiques  [43]  and Clowdr  [44]  in Compute Canada's HPC cluster environment. MCA instrumentation was achieved through Verificarlo  [26]  available on Github at https://github. com/ verificarlo/verificarlo. A set of MCA instrumented software containers is available on Github at https://github. com/gkiar/fuzzy.
The unprocessed dataset is available through The Consortium of Reliability and Reproducibility (http://fcon_1000. projects. nitrc. org/indi/enhanced/), including both the imaging data as well as phenotypic data which may be obtained upon submission and compliance with a Data Usage Agreement. The connectomes generated through simulations have been bundled and stored permanently (https://doi. org/10. 5281/ zenodo. 4041549), and are made available through The Canadian Open Neuroscience Platform (https:// portal. conp. ca/search, search term "Kiar"). All software developed for processing or evaluation is publicly available on GitHub at https://github. com/ gkpapers/.
A total of 783 OMUs were used as modelling units for distribution models (complete list in Appendix 4). The mimicry classification of all 1511 subspecies is available from Zenodo at https://doi. org/10. 5281/zenodo. 5497876. To compute indices of phylogenetic diversity, we used a recently published time-calibrated phylogeny of the Ithomiini  (Chazot et al. , 2019; Figure S3. 6) , which represents 339 out of the 388 species with georeferenced records.
27. 8 km × 27. 8 km. This resolution is appropriate for niche models based on large-scale predictors such as climate (McGill, 2010) , limits commission errors (Di Marco et al. , 2017)  and appears sufficient to identify broad geographic patterns of diversity at a scale relevant to biodiversity conservation (e. g. Abreu-Jardim et al. , 2021; Gumbs et al. , 2020; Robuchon et al. , 2021; Roll et al. , 2017). We selected climate, represented by annual temperature and humidity levels and seasonality (MERRAclim v. 2. 0;Vega et al. , 2017), elevation (SRTM   Dataset v. 4. 1; Farr et al. , 2007)  and vegetation cover (GLCF; Sexton et al. , 2013) , as environmental predictor variables for distribution modelling. Indeed, these environmental dimensions have been regarded as important in determining large-scale distribution patterns.
ME acknowledges funding by the  ANR  grant  CLEARWING  ( ANR-16-CE02-0012 ) and a  Human Frontier Science Program  grant ( RGP0014/2016 ). AVLF acknowledges the  FAPESP (Biota-FAPESP  grants  2011/50225-3, 2012/50260-6  and  2013/50297-0 ), the  Brazilian CNPq  ( 563332/2010-7  and  303834/2015-3 ) and  United States Agency for International Development (USAID)  and the  U. S. National Academy of Sciences (NAS)  under the  PEER program  (Mapping and Conserving Butterfly.
FLMNH  Museum Associates ;  Brazilian CNPq , Grant/Award Number:  563332/2010-7  and  303834/2015-3 ;  Darwin Initiative ;  National Geographic Society , Grant/Award Number:  5751-96 ;  National Science Foundation , Grant/ Award Number:  0103746 ,  0639977 ,  0639861  and  0847582 ;  U. S. National Academy of Sciences ;  Agence Nationale de la Recherche , Grant/Award Number:  ANR-16-CE02-0012  (CLEARWING);  United States Agency for International Development ;  Human Frontier Science Program , Grant/Award Number:  RGP0014/2016 ;  Fundação Amazônia Paraense de Amparo à Pesquisa , Grant/ Award Number:  2011/50225-3  and and map biodiversity in order to prioritize conservation efforts. 2012/50260-6;  French Ministry of Research (MENSR) ;  Leverhulme Trust.
DATA AVA I L A B I L I T Y S TAT E M E N T All R scripts are available on GitHub at https://github. com/MaelD ore/ithom iini_diver sity. Species-grid-cell records and mimicry classification used for modelling are available from Zenodo at https:// doi. org/10. 5281/zenodo. 4696055 and https://doi. org/10. 5281/ zenodo. 5497876. All OMU/species/mimicry ring modelled distribution maps are available from Zenodo at https://doi. org/10. 5281/ zenodo. 4673446. O RCI D Maël Doré https://orcid. org/0000-0003-3242-9242 R E FE R E N C E S.
β-SSNMF has shown itself as a powerful one to tackle blind HU, hence this comparative study between Algorithm 1 and GR-NMF  [13]  focuses on the convergence aspects including the evolution of the objective function and the runtime. As for all tests performed in this paper, the algorithms are tested on a desktop computer with Intel Core i7-8700@3. 2GHz CPU and 32GB memory. The codes are written in MATLAB R2018a, and available from https://sites. google. com/site/nicolasgillis/. The algorithms are compared for the following values for β P 0, 1  2 , 1, 3 2 , 2 (. For all simulations, the algorithms are run for 20 random initializations of W and H (each entry sampled from the uniform distribution in r0, 1s). Table  2  reports the average and standard deviation of the runtime (in seconds) as the final value for the objective function over these 20 runs for a maximum of 300 iterations.
Numerical experiments In this section, we perform numerical experiments to evaluate the effectiveness of Algorithm 3 on the HU problem. To the best of our knowledge, sparse β-NMF 5  from  [29]  is the most recent algorithm that is able to tackle problem  (32)  for the KL-divergence by integrating the 2 -normalization for each update of matrix W. This approach is similar to that of  [13]  for β-SSNMF, that is, it uses parametrization, and resort to a heuristic with no guarantee on the decrease of the objective function. We refer to this algorithm as β-SNMF. We apply Algorithm 3 and β-SNMF  [29]  to the three real hyperspectral datasets detailed in Section 3. This comparative study focuses on the convergence aspects including the evolution of the objective function and the runtime; we refer the interested reader to the Supplementary Material S2 for qualitative result on the ability of sparse β-NMF to decompose such images.
For simplicity, when "Voigt profile" is used alone without specifying "real" or "complex" hereafter, it refers to the "real Voigt" profile. The window function includes two tuning parameters that can offer much larger flexibility than standard symmetric window functions. In this article, we present the window function and its mathematical properties, derive the SnR expression with respect to its tuning parameters, and then show its performance based on both simulated data and real experimental data. We also suggest a general guideline for choosing the window function parameters, so that one can obtain close-to-optimal SnR and spectral resolution based on the properties of the chirped pulse dataset.
The Kaiser window, on the other hand, has to discard the data after a certain length in exchange for higher SnR, because the Kaiser window has a rigid symmetric window shape. (2) The FWHM. For all entries, the un-windowed spectra present the smallest FWHM. It is not surprising because applying window function in the time domain is equivalent to convolving the window function profile with the spectral line profile. Nevertheless, the Voigt-1D set (2) only broadens the line by approximately 25 %. These values demonstrate that the Voigt-1D set (2) window does not severely broaden the line in exchange for SnR enhancement. The FWHM produced by Voigt-1D set (1) is similar to that produced by Kaiser window with πα = 4. The FWHM is almost doubled. Finally, Kaiser window with πα = 8 produces 2. 5 times broader FWHM.
Performance of the Voigt-1D window is evaluated by treating real chirped pulse experimental data of OCS and CH 3 CN lines, and by treating simulated broadband chirped pulse data. The results are compared with un-windowed magnitude Fourier transform spectra, and with results treated by Kaiser-Bessel windows, which are commonly used in current chirped pulse literature. Our results show that the Voigt-1D window with maximum SnR/FWHM is able to enhance the SnR by 100 % on average, and sometimes up to 250 % than the un-windowed magnitude spectra, at a cost of only 25 % wider FWHM. The Voigt-1D window with maximum SnR can achieve slightly higher SnR enhancement at the cost of almost doubling the FWHM of the un-windowed spectra. Compared with Kaiser window (πα = 4), the SnR enhancement of the Voigt-1D window is higher, whereas the FWHM broadening is lower.
Supplementary material Supplementary material includes additional mathematics of the Voigt-1D window, experimental, simulation, and data fitting details, as well as some supplementary results such as the performance of "averaged" window parameters on broadband chirp. The supporting Python code for the optimization of Voigt-1D window function parameters is available at https://doi. org/10. 5281/zenodo. 4555759 and from the authors upon reasonable request.
Acknowledgement The authors thank the anonymous referees for helpful comments that improved the quality and robustness of this manuscript. This work was funded by the French ANR Labex CaPPA through the PIA under Contract No. ANR-11-LABX-0005-01, the Regional Council of Hautsde-France, the European Funds for Regional Economic Development (FEDER), and the contract CPER CLIMIBIO. L. Zou   In this section, we demonstrate the deviation of spectral lineshape from Voigt profile for the magnitude FT of an FID signal. We then prove that the Voigt-1D corrects the lineshape back to Voigt profile. To start, consider the envelope of a pure exponential FID: f (t) = e -bt , t ≥ 0. It can be also viewed as f (t) = u(t)e -|b|t : the product of the two-sided exponential decay e -b|t| , which is an even function, and the Heaviside unit step function u(t).
The experiment measurements of the OCS lines we used in this article are those reported in Zou et al. [4]. In those experiments, the lines were measured using a "dual direction mode" that alternates the frequency sweep direction. In this paper, however, we separated the FID data of the two directions, and treated them separately, so that the FID signal and the spectral lineshape in the frequency domain can both be unambiguously modeled. The experiment measurement of the CH 3 CN lines was conducted at room temperature in a cell of 1 m long. The cell was designed for pressure-broadening experiment and its pressure was monitored by a MKS 627A baratron. CH 3 CN (Sigma Aldrich) vapor was first introduced to the cell without additional treatment, and then slowly pumped out to reach the desired pressure of 4 µBar.
FID fit The FID fit was performed using the lmfit module. For OCS lines, the FID only contains one frequency component. There are several ways to construct the model equation, depending on how the DAQ delay time t 0 is expressed. Ideally, one would write f (t) = s exp(-a 0 (t + t 0 ) 2 -b 0 (t + t 0 )) sin(2πf if (t + t 0 ) + φ) + p 0 ( 15 ) where a 0 and b 0 are the initial parameters that describes the FID envelope, f if = |f lof s | is the intermediate frequency, f s is the line frequency and f lo is the local oscillator frequency, φ is the initial phase, s is the intensity scalar, and p 0 is the baseline drift. To avoid numerical instability, we simplified the above equation to f (t) = s exp(-a 0 t 2 -b 0 t) sin(2πf if t + φ) + p 0 (16) so that t 0 is merged into the effective intensity s and phase φ terms.
Spectral fit The spectral fit was also performed using the lmfit module. The frequency domain Voigt profile was defined as v(x; x 0 , γ G , γ L ) = Re wofz x + iγ L /2 √ 2σ , σ = γ G 2 √ 2 ln 2 (19) where γ G , γ L are the FWHM of Gaussian and Lorentzian components, and wofz(z) is the Faddeeva function, provided by the scipy. special. wofz function. The FWHM of the line was calculated using fitted γ G and γ L values, and the approximation γ V = 0. 5346γ L + 0. 2166γ 2 L + γ 2 G  [3]. The frequency domain complex Voigt profile vc(x) was defined using the identical Faddeeva function as in Equation 19, by replacing the Re operation by taking the magnitude of the function. The FWHM of the complex Voigt profile was determined numerically, by finding the root of vc(FWHM/2) = vc(0)/2. For numerical stability, the least-square fit was performed under a normalized condition.
The CH 3 CN fit When targeting high SnR, the closely-spaced hyperfine lines of CH 3 CN can cause a pitfall for the Voigt-1D window parameter selection, because of the interaction of the slowly varying beating envelope of the original FID signal, and the rapid rise of the window function profile. To demonstrate the complicated effect, we tested the treatment of Voigt-1D window with two FID signals. The two FID signals are identical data set, except for the DAQ delay time, one for 256 ns (presented in Figure  4  in the main article), and another for 450 ns (see Figure  S3 ). By altering the DAQ delay time, we can evaluate the effect of the node of the beating envelope. Following the convention in the main article, the Voigt-1D parameter set (1) optimizes for maximum SnR, and set (2) optimizes for maximum SnR/FWHM.
However, the 450 ns delayed data shows asymmetric lineshape. The results of Voigt-1D window set (1) and (2) on the two FID signals all show asymmetric lineshape. The parameter set  (1) , which is optimized for a larger b value, causes more severe lineshape imperfection than the parameter set  (2). When fitted with the Voigt profile, either no hyperfine structure can be resolved (256 ns delayed data), or the relative intensities of the two frequency components are far from correctness (450 ns delayed data). On the contrary, the truncated Kaiser window generates reliable results in both cases, with partially resolved frequency components with correct relative intensity. The drawback is that the total FWHM of the lines treated by the truncated Kaiser window is quite large. Therefore, the hyperfine structure is not really "resolved", as one peak may also be sufficient to fit the spectra line, and therefore the SnR is in fact the sum of two frequency components.
thanks the financial support from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie Individual Fellowship grant No. 894508. Supplementary Material for Window Function for Chirped Pulse Spectrum with Enhanced Signal-to-noise Ratio and Lineshape Correction Luyao Zou a , Roman A. Motiyenko 1, * a Université de Lille, Faculté des Sciences et Technologies, Département Physique, Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, 59655 Villeneuve d'Ascq Cedex, France 1. The magnitude Fourier transform (FT) of the FID.
thanks the financial support from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie Individual Fellowship grant No. 894508. Supplementary Material for Window Function for Chirped Pulse Spectrum with Enhanced Signal-to-noise Ratio and Lineshape Correction Luyao Zou a , Roman A. Motiyenko 1, * a Université de Lille, Faculté des Sciences et Technologies, Département Physique, Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, 59655 Villeneuve d'Ascq Cedex, France 1. The magnitude Fourier transform (FT) of the FID 7. Contributor Statement Luyao Zou: Methodology, Investigation, Formal anal- ysis, Visualization, Writing -Original Draft, Writing -Re- view & Editing. Roman Motiyenko: Conceptualization, Methodology, Writing -Review & Editing, Supervision.
In the ocean, the sea ice model LIM3 is used with one category of ice (IPSL-CM6-LR uses five ice categories based on ice thickness; see  Rousset et al. , 2015 , for more details on LIM3 in the mono-category). The land surface model ORCHIDEE was removed to simplify and speed up the implementation of the Schwarz algorithm. As a soil model, we use the simple bucket model included in the atmosphere code  (Ducoudré et al. , 1993). The specificity of IPSL-CM6-SW-VLR with respect to IPSLCM5-A2-LR and IPSLCM6 is given in Table  1. This specific version of the model is called IPSL-CM6-SW-VLR for further reference, with SW standing for Schwarz. A short evaluation of the performance of IPSL-CM6-SW-VLR is given in Appendix A.