dataesr/scientific-paragraphs-categorization huggingface dataset:
The improvement is consistent despite very different modality needs, network architectures, and training datasets. Moreover, the convolution operation modification appears robust. The gain in the error metric exceeds 3% on each modality except on the Flow360 dataset. The lack of periodicity in the estimated optical flow can explain this Flow360 smaller gain. The spherical optical flow is periodic, but the network did not learn this information when learning the perspective. Thus, the estimation of the road pixel flow is still inaccurate. This lack of periodicity remains one of the limitations of this adaptation method for optical flow networks. However, modified convolutions still improve the predictions, especially in the case of single-object flow prediction, as shown in the following qualitative study.
Semantic Segmentation This section compares the semantic segmentation estimation differences between the adapted and baseline networks. Looking at the set of predictions made on the RWFOREST dataset, we notice two main improvements: better detection of the shapes in the polar regions and a less erroneous class estimation. Figure  5  shows the two prediction samples used to illustrate these results. First, the spherical adaptation helps the network to take into account equirectangular distortions. The detection of shapes and objects is improved in highly distorted regions thanks to a better local coherence of the pixels. This effect is visible in sample 1, where the adapted network better identifies the tree canopy (upper polar region of the image). In addition, the adaptation also reduces the number of noisy predictions.
Optical Flow The optical flow enhancements are clearly visible as objects move into the polar regions of the equirectangular image. Figure  9  shows two optical flow estimates in the dataset Flow360. In both examples, the car passes under a streetlight. Due to the improved local pixel coherence provided by the distortion-aware convolutions, the adapted network is able to track the path of the streetlight in the upper polar region of the image. As a result, the estimated optical flow is close to the ground truth. In parallel, the non-adapted network has difficulty detecting this same streetlight. Consequently, the flow prediction is inaccurate in sample 1 or even empty in sample 2. For optical flow estimation in real images, we focus on the motion of a ball during a throw. Figure  10  shows two different image sequences with associated optical flow predictions.
more, this can easily overcome the lack of outdoor omnidirectional datasets. Finally, it allows us to keep up with the new architectures proposed regularly in deep learning for perspective images. For each comparison, the best results are in bold. RWFOREST 256 × 256 MIoU (↑) Semantic segmentation baseline 0. 677 0. 810 2. 045 Semantic segmentation adapted 0. 688 (+1. 525%) 0. 828 (+2. 282%) 0. 337 RWFOREST 512 × 256 MIoU (↑) Accuracy (↑) AECE (↓) Semantic segmentation baseline 0. 504 0. 631 3. 692 Semantic segmentation adapted 0. 564 (+11. 980%) 0. 639 (+1. 332%) 1. 577 RWFOREST 1024 × 512 MIoU (↑) Accuracy (↑) AECE (↓) Semantic segmentation baseline 0. 443 0. 621 5. 845 Semantic segmentation adapted 0. 528 (+19. 174%) 0. 627 (+0. 852%) 3. 034 Accuracy (↑) AECE(↓).
To address this issue, we present a new data-driven method for correcting systematics in RV data. We focus our work on data collected with the SPIRou instrument, a high-precision RV spectrograph in the near-IR domain with two science topics that are at the forefront: the quest for Earth-like planets in the habitable zones of very-low-mass stars, and the study of low-mass stars and planet formation in the presence of magnetic fields  (Donati et al. 2020). To achieve these science goals, SPIRou has a large program (LP) called the SPIRou Legacy Survey (SLS) 1 which was allocated 310 nights over seven semesters (2019a to 2022a) on the Canada-France-Hawaii Telescope. The SLS-Planet Search program, which is a part of this LP, aims to detect and characterize planetary systems around ∼50 nearby M dwarfs  (Moutou et al.
, in prep. ). The SPIRou data are prone to the previously mentioned systematics and it is necessary to develop methods to correct them. Our method, Weighted-principAl comPonent analysIs recon-sTructIon, referred to as Wapiti 2 , is agnostic to the origin of the systematics and reconstructs the per-line RV time series. This method takes advantage of the new line-by-line (LBL) algorithm  (Artigau et al. 2022 ) used to compute RV data with SPIRou, which provides a RV time series for each line of the spectrum. The application of principal component analysis (PCA) to mitigate systematics in RV data is a well-established technique in the exoplanet community. However, existing methods are primarily aimed at specifically reducing the impact of stellar activity, such as the methods presented in Collier Cameron et al.
(  2021 ) and 1 https://spirou-legacy. irap. omp. eu/doku. php 2 https://github. com/HkmMerwan/wapiti  Cretignier et al. (2022). PCA based methods were also explored to correct for telluric or instrumental effects in prior studies  (Artigau et al. 2014; Cretignier et al. 2021). Our method, on the other hand, is unique in that it does not focus solely on reducing the impact of stellar activity or telluric effects but instead is a versatile and flexible approach that can be applied to any target, as long as LBL data are available. We demonstrate the effectiveness of Wapiti by applying it to the star GJ 251, a target with a known planet in the SLS-Planet Search program. This paper is structured as follows. Section 2 provides an overview of the observations, data reduction, and LBL algorithm used for the study.
0 ± 0. 4 M ⊕ and an equilibrium temperature of T eq = 351 ± 1. 4 K  (Stock et al. 2020). The small amplitude of this planet makes GJ 251 an ideal candidate to demonstrate that SPIRou is also a suitable instrument for detecting Earth-like planets in the habitable zone of M dwarfs. The observations were collected as series of circular polarization sequences of 4 individual sub exposures per night. The data collection for GJ,251 spans from December 12, 2018 to April 14, 2022, comprising a total of 769 subexpositions, with each visit comprising four subexposures. Out of the available data, three visits are incomplete, leaving us with a total of 191 complete visits. The airmass during these observations varied from a minimum of 1. 028 to a maximum of 2. 003, with a median value of 1. 083. The signal-to-noise ratio per 2.
The LBL method has been compared to other methods such as the cross-correlation function and template matching in  Martioli et al. (2022)  and  Artigau et al. (2022). For each spectrum, the LBL algorithm combines the velocities of individual lines (27 702 lines in the case of GJ 251) into a single RV measurement. This is achieved using a mixture model, which assumes that the velocities of individual lines are distributed according to a Gaussian distribution centered on the mean velocity, or another distribution of high-sigma outliers with multiple origins (e. g. , bad pixels, cosmic rays, telluric residuals). The RV measurements are grouped by night by calculating the inverse-variance weighted mean of all observations for each night, resulting in a reduction from 769 to 177 data points. To address the variation in velocities of the day-to-day drift, a correction is applied using simultaneous Fabry-Pérot measurements.
Furthermore, to take into account any long-term variation, a Gaussian Process (GP) regression was computed using the most observed stars in the SLS in order to estimate the zero point in the time domain. This procedure is similar to the one conducted for SPIRou data in  Cadieux et al. (2022)  or for SOPHIE  (Courcol et al. 2015) , HARPS  (Trifonov et al. 2020)  and HIRES  (Tal-Or et al. 2019)  spectrographs. In our case, we employed the celerite package  (Foreman-Mackey et al. 2017)  to fit a GP model using a Matérn 3/2 kernel. The estimation of the hyper-parameters was achieved by minimizing the likelihood function. Studies on common trends in SPIRou data are being conducted in parallel, and will address the differences between GPs and more commonly used tools such as a running median or nightly offsets in forthcoming work by the SPIRou team.
The Wapiti method Our approach applies a PCA to the per-line RV time series produced by the LBL algorithm. Since these datasets may be noisy and contain missing data, we use the weighted principal component analysis (wPCA) method described in  Delchambre (2015) , implemented in the wpca module 3  and each observation is weighted by the inverse of its uncertainty squared. The objective of the Wapiti method is to eliminate the sources of systematic error. This is achieved by performing a wPCA reconstruction of the original per-line RV time series and subtracting its reconstructions from it. The rationale behind this approach is that, in a time series dominated by spurious signals of unknown origin, selecting appropriate components can serve as a proxy for correcting the effects responsible for the resulting systematic errors.
To determine the appropriate number of principal vectors, we suggest the following approach. First, we discarded all individual line RV time series that have more than 50% of missing data, reducing the number of lines from 27 201 to 17 923. Such missing data may occur for a line when the RV value deviates by more than five sigma from the standard deviation in relation to the line's RMS  (Artigau et al. 2022). Subsequently, we binned each individual per-line RV time series by night, by computing the inverse-variance weighted mean of all observations for each night. Afterward, we night-binned in a similar fashion the Fabry-Pérot drift also computed with the LBL and removed it from each individual per-lines RV time series. Finally, we standardized the time series using their inverse-variance weighted mean and variance.
Reducing the number of components through a permutation test The selection of the appropriate number of components for a wPCA is a critical aspect. Too few components may fail to effectively remove undesired contamination, while an excessive number of components may lead to over-fitting and an increase in the levels of random noise. To address this issue, a method is needed to determine which wPCA components are relevant and necessary for the analysis. In our work, we first used a permutation test  (Vieira 2012 ) which involves independently shuffling the columns of the dataset, and then conducting a wPCA on the resulting dataset. We repeated this process 100 times and compared the explained variance of the original dataset with the permuted versions. If a principal component is relevant, we expect that the permuted explained variances of that component will not be greater than the original explained variance.
Leave-p-out cross-validation To evaluate the significance of the number of components retained after the permutation test, we conducted a leave-p-out cross-validation. This approach has been used by  Cretignier et al. (2022)  to select relevant components, albeit with variations in the methodology. In this study, we generated 100 subsets of the per-lines RV dataset, each containing 80% of the lines randomly selected. The wPCA was then recalculated for each of these N datasets to assess the robustness of the 26 remaining components. The underlying idea involves evaluating the robustness of the eigenvector basis, also known as principal vectors, by examining their stability under the removal of a few lines. Should a principal vector exhibit excessive sensitivity to the lines in use, it is deemed superfluous and may be discarded.
We employed the Pearson coefficient of correlation as the evaluation metric, for the reasons stated in  Cretignier et al. (2022)  being that it is computationally efficient, bounded, and insensitive to the amplitudes of vectors. Specifically, we computed the Pearson coefficient between the nth principal vector obtained from the wPCA using the full dataset and the nth principal vector obtained from each of the N subsets. The absolute value of the coefficient was taken, as the wPCA vectors may change sign. The median Pearson coefficient value was calculated for each component number, and only those with a value above an arbitrary threshold of 95% were retained, as in  Cretignier et al. (2022). As depicted in Fig. 3 , it was observed that the value first goes below the threshold after the 13th component.
This indicates that the principal vectors after the 3th one are not correlated with their corresponding vectors in the original dataset, implying that these eigenvectors are reliant on the lines used. As a result, they were disregarded, leaving us with 13 components for the remainder of the Wapiti method. In future research, efforts will be conducted to study how the number of components obtained through the application of the two methods, namely the permutation test and the leave-p-out cross-validation, varies with the target being studied.
(1) Consequently, we reorganized the epochs in a descending order based on the value of D, resulting in a list that ranks the degree of anomaly of each observation. We chose to discard the first N elements from this list. To identify the optimal value of N, we gradually removed them one by one and determined the number that maximizes the significance of the signal in the corrected RV once the Wapiti method had been applied. We found that removing the first seven outliers produced the best outcomes, reducing the time series from 178 to 171 data points. It is acknowledged that readers may perceive this method to be specific to individual stars. However, we contend that this is a justifiable approach for our selected target GJ 251, as the signal remains consistent regardless of the number of rejected outliers.
Moreover, the main benefit of this approach is that it provides a framework to assess the level of anomaly for any target at a given epoch. For further information about this process, refer to Appendix A. The top-left panel of Fig. 4  displays the RV time series with flagged outliers highlighted in red. The periodogram of the RV time series after the removal of outliers is displayed on the right. Furthermore, the first two principal vectors are presented on the left, with the previous principal vectors using all available data points depicted in red, and the new principal vectors obtained from applying the wPCA on the remaining data points shown in black. The periodograms of the new principal vectors are displayed on the right. From the periodograms, it can be observed that the presence of a 1-yr period and a 180-day period is evident in the two vectors, indicating that the wPCA method identified signals within the per-line RV dataset that may be contributing to the resulting systematic errors.
The Wapiti corrected time series and its analysis The method outlined in the previous section has allowed us to determine the most appropriate number of components for our dataset on GJ 251. We subsequently subtracted the reconstruction of the original time series to itself to generate a new time series, which we refer to as the Wapiti corrected time series. We evaluated the effectiveness of the correction by analyzing the resulting periodogram as illustrated in Fig. 5. In this figure, the time series resulting from the correction is depicted in blue and the original data are represented in black. The same color scheme is used when plotting the periodograms below the time series. As desired, the Wapiti correction effectively eliminated the 180 d and 365 days peaks that we attributed to systematics present in our data since those periods are no longer statistically significant and the planet previously reported by  Stock et al.
(2022)  and listed in Table  1. One may note that the eccentricity is poorly constrained from our RV data, prompting the question of whether a circular fit would yield a better result. To address this, we conducted a comparison of the maximum likelihood estimation (MLE) for both Keplerian and circular models, allowing us to compute their respective Bayesian Information Criterion (BIC; see  Schwarz 1978). By taking the logarithm of the Bayes factor (log BF = BIC circ. -BIC kep. 2 ), we were able to compare the two models. Our analysis strongly favored the Keplerian model (log BF = 15), and as such, we decided not to perform a MCMC estimation of the orbital parameters using a circular model. The phase-folding of the best-fitted model to the data is displayed in Fig. 6  which also present the periodogram of the residuals with no significant signals within it.
The results from both our data and  Stock et al. (2020)  demonstrate that the impact of stellar activity on RV data can manifest with a ∼2σ difference to the periodicity reported in  Fouqué et al. (2023)  when studying B ℓ. This indicates that the effect of stellar activity on RV data may not always occur at the same period, for instance due to differential rotation, and must be evaluated with available indicators on a case-by-case basis.
Discussion, summary, and prospects The Wapiti method successfully eliminated the spurious signals in the GJ 251 data and detected the planetary signal. Although our study demonstrated the effectiveness of the method in accurately estimating planetary parameters, it is important to carefully consider the characteristics of the data. For instance, in situations where a high semi-amplitude planetary signal or trend is present, it would be recommended to first fit these signals and then apply the method to the residuals. Furthermore, due to its data-driven nature, this method does not require a model for the origins of the corrected systematic A187, page 8 of 18  M. , et al. : A&A proofs,. Analysis of dLW and W1 time series. The left panels display, at the top, the dLW time series and its corresponding periodogram at the bottom, which shows no indication of periodicity in the data.
A BERV effect in SPIRou LBL RVs of GJ 251 From the outset of our study, it was apparent that the spurious signals at 180 and 365 days in our dataset could be attributed to a residual telluric effect, as verified through visual examination of the data in the BERV space in Fig. 9. This analysis revealed the presence of a BERV effect, with significant fluctuations occurring in the original data at BERV values of approximately 10 and 25 km s -1. It is worth noting that the largest fluctuation observed in our data corresponds to a velocity of the star that is close to zero in the observer's frame of reference due to the star's velocity of 22. 98 +0. 22  -0. 22 km s -1. The principal vectors successfully captured the BERV dependency, as evidenced by an evident structure in the BERV space. For the sake of readability we only displayed the first three vectors in Fig.
Investigating the sources of systematics An approach to search for the underlying physical causes of systematic variations in our data would be to examine the scores obtained from the wPCA. These scores represent the transformed data in the new coordinate system established by the principal vectors. To quantify the influence of a specific principal component on a given line, we examined its score values U n. Our method involved computing the value Ũn = U n -Ūn σ(U n ) , where Ūn and σ (U n ) denote the weighted mean and uncertainties of U n , respectively. For each line λ, we determined the maximum absolute Z-score value of Ũn (λ) over all the components. Recall that the Z-score of a value x in a sample with mean µ and standard deviation σ is given by Z(x) = x-µ σ. Hence, the metric we employed to quantify the extent to which a line is affected by the systematics is determined for each line λ as follows: z (λ) = max n |Z Ũn (λ) |.
Based on our analysis, we observed that 14 atomic lines (in blue), 8 OH lines (in red) and 9 CO lines (in green) could correspond to the affected lines, which accounts for 50% of the total affected lines. Furthermore, we observed that 27 of those lines that have a potential association with the star are located in the H band. For the remaining lines located in the telluric region, our findings suggest a possible complex interplay between telluric and stellar lines. Specifically, the overlapping of molecular or atomic lines with telluric lines may explain 4 https://github. com/njcuk9999/apero-drs/tree/main/ apero/data/spirou/telluric why both a 1-yr signal and the star's rotational period can be distinguished in V 1. However, the origin of the 32 remaining lines with a z value above 10 is uncertain, some of them could be molecular lines as of yet unidentified but also of a completely different origin.
Conclusion and future work In this paper, we have presented Wapiti, a new data-driven algorithm for correcting systematic errors in RV data. The algorithm used a dataset of per-line RV time series generated by the LBL algorithm and employed a weighted principal component analysis to subtract the wPCA reconstruction from the original data. This process created a new RV time series free of systematic errors. To determine the appropriate principal vectors, the algorithm incorporated a permutation test followed by leave-p-out cross-validation algorithm. Once the relevant number of components have been identified an outlier rejection step followed and the wPCA was applied to the remaining data points. The wPCA reconstruction was consequently removed from original RV time A187, page 10 of 18 Fig.
Acknowledgements. This project received funding from the  European Research Council  under the  H2020 research & innovation program  (grant # 740651  New-Worlds). E. M. acknowledges funding from  FAPEMIG  under project number  APQ-02493-22  and research productivity grant number  309829/2022-4  awarded by the  CNPq, Brazil. J. H. C. M. is supported in the form of a work contract funded by  Fundação para a Ciência e Tecnologia (FCT)  with the reference  DL 57/2016/CP1364/CT0007 ; and also supported from  FCT  through national funds and by  FEDER-Fundo Europeu de Desenvolvimento Regional  through  COMPETE2020-Programa Operacional Competitividade e Internacionalização  for these grants  UIDB/04434/2020 & UIDP/04434/2020 ,  PTDC/FIS-AST/32113/2017  &  POCI-01-0145-FEDER-032113 ,  PTDC/FIS-AST/28953/2017  &  POCI-01-0145-FEDER-028953 ,  PTDC/FIS-AST/29942/2017.
Database We used the brain MRI dataset from the Human Connectome Project (Q1-Q4 release, 2015) acquired by Washington University in Saint Louis and University of Minnesota  [39]. This database includes 1065 healthy subjects aged from 22 to 35 years, who all underwent an anatomical T1-weighted (T1w) with a 0. 7mm spatial isotropic resolution and series of diffusion MRI (dMRI) scans using 3 different b-values of 1000, 2000, and 3000 s/mm2 and 90 diffusion directions per b-value shell, with a 1. 25mm spatial isotropic resolution, conducted on a 3T MRI scanner. The data were already preprocessed and corrected for eddy current and susceptibility artifacts.
The authors also performed a multiple regression analysis, showing that the distance between the temporal pole and the tip of Meyer's loop was an independent predictor of postoperative visual field defect (β = -0. 80). Finally, in a study [32] of 30 healthy subjects using a 3T MRI scanner and a probabilistic tractography technique, the mean distance between the rostral ridge of optic radiations and the tip of the temporal pole was 23. 1 mm in the left hemisphere, and 26. 41 mm in the right hemisphere, more in line with the dissection studies and ours. The results of those studies, as well as a few other tractography studies  [8, 33, 36, 40] , are summarized in table  1. With our methodology combining a large number of individuals, a high-resolution angular and spatial diffusion MRI dataset and a state-of-the-art diffusion analysis methodology, we found a better agreement with histological data, demonstrating the reliability of such in vivo studies.