dataesr/scientific-paragraphs-categorization huggingface dataset:
According to the authors, reads were demultiplexed using Cell Ranger v2. 0, and cells with fewer than 500 genes or 1000 UMIs were discarded, ending up with 65,667 valid cells. We preprocessed the three raw count matrices independently. First, each cell was normalized to 10,000 counts, and log(1 + x) transformation has been applied according to the existing preprocessing standards. We pooled each cell to the average of its 5 nearest neighbors (using Euclidean metric in the space of the dataset's 30 first principal components) to reduce noise. Eventually, we selected the 10,000 most variable genes in each dataset to end up with three preprocessed expression matrices, each expressed in a 10,000 feature space. Lung tissue contains a complex, hierarchical population of cells of various types and states organized into different compartments.
Strong differences in specific genes expressed in each of these compartments cause cell-associated gene expression vectors to form more or less compact clusters in the multi-dimensional gene space (see Figure  7A, B. We can see data point clouds corresponding to the three lung datasets do not overlap even when looking at cells from different datasets associated with the same compartment. We suggest using DAPCA instead of standard PCA to carry out dimensionality reduction, taking into account the author-provided cell annotations (endothelial, stromal, epithelial and immune). We set the first dataset to be the source domain, as it contains the largest number of cells, and we consider the union of the two other datasets to be the target domain. DAPCA is aimed at finding a low-dimensional linear projection (with only a few tens of features) in which the multivariate distribution of projections from different samples would appear as similar as possible, while cells with labels related to different compartments would be maximally separated.
Application of DAPCA in such context is shown in Figure  7A. Visual inspection of the resulting projections into the first 30 components extracted by PCA, SPCA and DAPCA and further visualization using UMAP shows that the DAPCA projections overlap much better than PCA and SPCA projections (Figure  7A , top panels). At the same time, the separation between cell types remains well preserved (Figure  7A , bottom panels). In order to quantify the effect of domain adaptation, we trained a simple kNN classifier (k = 20) to predict the dataset of origin of each cell within the DAPCA representation. We expect the classifier to perform poorly when domain adaptation is successful, meaning that the source and target datasets are indistinguishable. It also makes sense to normalize the performance of such classifier with respect to its baseline level accuracy which can be estimated by randomly permuting the labels of the datasets.
Both absolute and normalized accuracies are shown in Figure  7C. Comparison between PCA, SPCA and DAPCA using this strategy allows confirming that DAPCA outperforms the two other methods at making cells less distinguishable with respect to their dataset of origin. We also observe DAPCA does not merge equally well the cells belonging to different compartments (Figure  7C ). For instance, domain adaptation applied to endothelial cells appears to be close to the theoretical optimal performance. On the other hand, domain adaptation applied to the cells from the stromal compartment was less good. This could be explained by the high heterogeneity within the cells annotated as stromal, which are grouped into four different clusters. We followed this first analysis step by extracting the subparts of the datasets corresponding to the stromal cells and we applied PCA, SPCA, and DAPCA to this subset of cells.
In order to apply SPCA and DAPCA we defined new labels in Dataset 1 serving the source domain, by clustering it with the standard Louvain clustering algorithm (these clusters are shown in color in Figure  7B ) such that the clusters hypothetically correspond to major subpopulations within the stromal cell compartment. Four such subpopulations have been identified. The DAPCA-based domain adaptation in this case shows the performance close to be optimal (Figure  7D ). Interestingly, three out of four clusters seemed to match and at least partially mix with the cells from the target domain (Datasets 2 and 3). One of the clusters appeared to remain specific to the source domain (Dataset 1), and could correspond to a subpopulation of lung cells specific to dataset 1, and located in the stromal compartment.
Overall, we can conclude that DAPCA can be used as a tool for simultaneously integrating scRNA-seq datasets from different origins as well as reducing their dimensionality, as long as cell annotations are available for at least one dataset. We furthermore showed DAPCA is able to preserve cell-cell similarity in a biological sense, meaning cells within similar compartments and expression profiles remain close to one another after the algorithm application. Compared to other widely used techniques, DAPCA is based on linear dimensionality reduction which does not tend to overfit the data integration task. In particular, it naturally allows one to consider the existence of specific parts in the source or in target domains that can have specific biological properties and should not be easily matched between the source and the target domains.
Discussion In this paper, we suggest a novel base linear method for solving the problem of domain adaptation which can serve as a preprocessing step for the application of more sophisticated and non-linear machine learning approaches. The method is named Domain Adaptation Principal Component Analysis (DAPCA) because it represents principal component analysis generalization. As input DAPCA takes a pair of two datasets (source X and target Y), one of which is labeled (source) and another is not (target). Formally, one of these datasets can be empty. If the target domain Y is empty then DAPCA degenerates to the supervised PCA in the source domain X. If the source domain X is empty, DAPCA degenerates to the standard PCA in the target domain. If the source domain X contains only one label then DAPCA represents a specific version of consensus PCA which can be used to solve the data integration task.
The classical domain adaptation problem (which is sometimes called unsupervised in the sense that no label information is available for Y) can be extended to the semi-supervised case (where partial information on labels in Y is known). DAPCA can be easily adapted to this situation, too, by introducing the proper weighting schema between pairs of data points. A large number of variables characterizes many modern datasets so that the corresponding data point clouds formally exist in high-or very high-dimensional space. A typical step in analyzing such datasets is a dimensionality reduction step to a more manageable number of dimensions (e. g. , few tens or even 3-4). For example, this is the typical case of omics data in the field of biology, including single-cell data  [38, 39]. If this number is close to an estimated intrinsic dimensionality  [40, 41]  of the data, then this step does not lead to a significant loss of information.
The reduction is frequently made through the use of the classical PCA. DAPCA allows a user to easily replace this step when the divergence between the source and the target datasets is suspected. In addition, it takes into account the labeling data. The iterative DAPCA also helps to resolve the classical distance concentration difficulty (curse of dimensionality): in really large dimensional distributions, the kNN search may be affected by the distance concentration phenomena: most of the distances are close to the median value  [42]. It was shown that the use of fractional norms or quasinorms does not save the situation  [43]. However, dimensionality reduction may help to overcome this. DAPCA is based on a data point matching step, where for each point from the target dataset one has to indicate the most similar, with appropriate metrics, data points from the source dataset.
Such an approach can find applications in many domains, such as bioinformatics or single-cell data science  [35]. As it was expected, our study shows that neural-network-based classifiers equipped with an adversarial module that tries to distinguish the source from the target domains (such as DANN) achieve better performance than the linear and more constrained DAPCA approach when tested on imaging data. This is partly explained by the fact that the convolutional layers of DANN are trained on the information from both source and target domains, while in our comparison DAPCA used the image representation trained on the source domain only. Linear methods such as DAPCA are deterministic, computationally efficient, reproducible, and relatively easily explainable. Therefore, the linear approaches occupy a niche in those machine learning applications where such features are more important than the maximum possible accuracy.
Funding: This work was supported by the  French government  under the management of  Agence Nationale de la Recherche  as part of the " Investissement d'avenir" program , reference  ANR-19-P3IA-0001  ( PRAIRIE 3IA Institute ), Part of this project was supported in 2020-2021 by the  Ministry of Science and Higher Education of the Russian Federation  (Project No. 075-15-2021-634 ). Institutional Review Board Statement: Not applicable.
Figures  1 2 3 show the absorption cross-section between 195 and 830 nm at T = 295 K. The data correspond to the spectra recorded by J. Malicet, J. Brion, and D. Daumont in the Groupe de Spectrométrie Moléculaire et Atmosphérique (GSMA) at the University of Reims in the 1970s, using a Jobin-Yvon monochromator, working at a resolution of 0. 01 nm, and are provided here as private communication. In addition to the spectrum shown in Figures  1 2 3 , these researchers recorded UV spectra at temperatures of  218, 228, 243 , and 273 K. The reader can find these spectra in the S&MPO database  [64]  at https://smpo. iao. ru/xsections (since 1 May 2005). More detailed information is given in  [60, [65] [66] [67] [68] [69] [70] [71].
Thus, a set of six numbers is used to label the vibration-rotation energy level (the numbers Ka and Kc are often used as subscripts of the number J)-(V1V2V3) J Ka Kc. The general form and structure of absorption bands in the spectrum of a molecule are determined by the selection rules for allowed transitions between various vibration-   One of the most complete resources on the vibrational-rotational absorption spectrum of the ozone molecule is the Internet accessible information-computing system "Spectroscopy and Molecular Properties of Ozone" (S&MPO) at https://smpo. iao. ru and https://smpo. univ-reims. fr (the last release of this database SMPO_20d is accessible since 1 De- cember 2020).
Thus, a set of six numbers is used to label the vibration-rotation energy level (the numbers Ka and Kc are often used as subscripts of the number J)-(V1V2V3) J Ka Kc. The general form and structure of absorption bands in the spectrum of a molecule are determined by the selection rules for allowed transitions between various vibration- One of the most complete resources on the vibrational-rotational absorption spectrum of the ozone molecule is the Internet accessible information-computing system "Spectroscopy and Molecular Properties of Ozone" (S&MPO) at https://smpo. iao. ru and https://smpo. univ-reims. fr (the last release of this database SMPO_20d is accessible since 1 December 2020).
Calculation of Energy Levels and Transitions The line lists, which are contained in many spectroscopic databases, usually result from analyses of experimental spectra based on effective models that, in the case of ozone, have been widely described in  [85] [86] [87]. These models are based on the Watson's type effective Hamiltonian  [88]  augmented by supplementary coupling terms  [89, 90] , accounting for resonance interactions, and on the effective transition dipole moment operator introduced by Flaud & Camy-Peyret  [91]. In most of the studies of high-resolution spectra of the ozone molecule, the rotational (reduced) Hamiltonian for vibrational states is used in the Watson's form  [88]. e f f H VV = E VV + A -1 2 (B + C) J 2 z + 1 2 (B + C) J 2 + 1 2 (B -C)J 2 xy -∆ K J 4 z -∆ JK J 2 z J 2 -∆ J J 2 2 -δ K J 2 z , J 2 xy -2δ J J 2 xy J 2 + H K J 6 z + H K J J 4 z J 2 + H JK J 2 z J 2 2 + H J J 2 3 +h K J 4 z , J 2 xy + h K J J 2 z , J 2 xy J 2 + 2h J J 2 xy J 2 2 + L K J 8 z +.
The "ASSIGN" code  [106] , based on GSCD, has been written to find this type of curve in real spectra and specific calculations. ( ) ( ) ( ) k V V t t t Z k k d μ ′  A  = (6) where V denotes the vibration state (V1V2V3), and ( ) t k d are the numerical coefficients de- termined either from the perturbation theory or by a fitting of computed line intensities to experimental ones. Rotation operators ( ) t k A depend on the type (t) of vibration band. The first eight operators of expansion (6) can be found in  [91]. Later Toth  [105]  published next eleven terms of expansion  (6). The progress in the recording of absorption spectra imposes increasingly high requirements on the quality of calculations of the VR structure for adequate modeling of these spectra.
The "ASSIGN" code  [106] , based on GSCD, has been written to find this type of curve in real spectra and specific calculations. In contrast to the toy example Figure  6 , the following Figure  7  represents a real case of the observed intersection of the rotational levels of the (  101 ) and (030) of the 17 O 18 O 18 O isotopologue (unpublished), that can occur between a bright and a "dark" state (the definitions of these two latest terms being explained in  [21] ), leading to a sharp resonance (∆Ka = 3 in this particular case). Such resonances allow information about the band center and the rotational constants corresponding to the dark state to be obtained, even though much less accurately than for the directly observed bands. Obviously, the quantity and quality of useful information directly depends on the number of resonances and their strengths.
The second method of rotational assignment of experimental spectra is the use of synthetic spectra. These spectra are plotted using calculated lists of frequencies and intensities of VR transitions and are directly compared with the observed spectra. For these purposes, we use the MultiFit code developed in the GSMA laboratory  [107]. This method has proven its high efficiency, particularly for the assignments of A-type bands in high wavenumber ranges (see Section 4. 4. Results).
Line Positions Empirical approaches to calculate VR line positions using least square fits of the EH parameters to experimental transitions, lead generally to a good agreement between observations and calculations on the order of several thousandths of the wavenumber, at least for vibrational bands up to three or four vibrational quanta. This corresponds to a relative precision in energy levels of 10 -7 or 10 -8 that is not nowadays accessible by first The second method of rotational assignment of experimental spectra is the use of synthetic spectra. These spectra are plotted using calculated lists of frequencies and intensities of VR transitions and are directly compared with the observed spectra. For these purposes, we use the MultiFit code developed in the GSMA laboratory  [107]. This method has proven its high efficiency, particularly for the assignments of A-type bands in high wavenumber ranges (see Section 4.
The DMS of  [133]  is currently considered to be the most accurate. It was used for ab initio scaling of the ro-vibrational intensities of thirty ozone bands, subsequently validated by atmospheric and laboratory measurements  [158]  and included in the last release of the S&MPO and HITRAN databases as described in  [18, 24]. This DMS was also used for a combined ab initio/empirical line list computed by University College London with collaborators  [159]. It is important to recall the following things. The uncertainty in the best variational calculations of the line positions using ab initio PESs is in the order of a few tenths of wavenumber. This represents a significant improvement but is still far from empirical accuracy. When local resonances occur, it is often the case that ab initio predictions might produce larger uncertainties in ro-vibrational patterns.
Data Reduction All research groups have their own software to derive the following experimental parameters: positions, intensities, self-broadening and/or pressure broadening by other gases (for example, air-broadening), and, ultimately, parameters of the line profile when the speed dependence is included  [174]. In all cases, the parameters are determined by minimizing the difference (Observed-Calculated) between the observed and calculated transmittances. The fits are performed sequentially for each line, adjusting the experimental parameters. In addition, 100% transmittance is determined (using a polynomial of degree 1 or 2), in a small interval of analysis (between 0. 01 and 0. 07 cm -1 , depending on the experimental conditions), and, if necessary, ILS-related parameters. The fits are consistently performed in the whole domain (up to 200 cm -1 ).
The second case was limited to a triad of interacting states including Coriolis interactions (105) ↔ (006) and (  105 ) ↔ (312). The band ν 1 + 5ν 3 (S VR = 4. 9 × 10 -23 cm/molecule) is at the highest edge of the range that we were able to record and analyze using FTS technique. The final results of all the analyses described in this section are empirical values of VR energy levels, fitted parameters of effective Hamiltonians and of effective transition moment operators and, finally, complete line lists computed from these parameters. The calculated lists include transition frequencies (ν ij ) and intensities (S ij ), lower energy values (E low ), and the quantum identification of upper and lower levels. Further, these lists, completed by the broadening (γ air , γ self ) and shifting (δ air ) parameters of spectral lines, are included in spectroscopic databases, such as the S&MPO  [18, 21, 64] , GEISA  [223] , and HITRAN  [24, 224, 225]  databases.
The spectrum studied to date reaches the region of 8000 cm -1 , about 93% of the dissociation threshold D 0 exp = 8560 cm -1  [122, 124]. There is a significant decrease in the intensity of the bands above 5800 cm -1 , which once again demonstrates the advantage of recording these spectra by the LiPhy CRDS setup  [33]  and of using theoretical predictions for the analyses. As mentioned above, the results obtained in the studies presented here (νij, Σij, Elow, VR assignment), augmented with additional parameters (γair, γself, δair) and coefficients of their temperature dependence (at least in the range from -70 °C up to +50 °C), are incorporated into spectroscopic databases (for example, S&MPO  [64] , GEISA  [223] , and HI-TRAN  [24] ). The use of spectroscopic bases for various atmospheric tasks, such as the simulation of atmospheric absorption and transmission spectra, determination of the total molecular column and altitude profiles of molecular concentrations, radiative transfer in the atmosphere, radiation blocks of climate models, etc.
, places increasingly high demands on the accuracy of the parameters of these databases and their completeness. As a rule, the data presented in the databases are a mixture of observations and calculations. Like in the case of line intensities of the ozone molecule, only a small part of the line broadening coefficients can be determined from the observed spectra. Then, it is necessary to use empirical models to interpolate or extrapolate to all quantum numbers that may be necessary for atmospheric tasks. One example of experimental measurements is given in  [180] , and the calculation is given in  [84]. The HITRAN database  [24]  provides individual references to the source for each of the six parameters of each transition: position, intensity, air-and self-broadening, air shift, and temperature dependence of the air-broadening.
The use of simplified models is due to the fact that there is no empirical information about many dark vibrational states and their parameters cannot be estimated with sufficient accuracy. These circumstances lead to deterioration in the quality of the description (an increase of RMS deviations). As mentioned above, the results obtained in the studies presented here (ν ij , Σ ij , E low , VR assignment), augmented with additional parameters (γ air , γ self , δ air ) and coefficients of their temperature dependence (at least in the range from -70 • C up to +50 • C), are incorporated into spectroscopic databases (for example, S&MPO  [64] , GEISA  [223] , and HITRAN  [24] ). The use of spectroscopic bases for various atmospheric tasks, such as the simulation of atmospheric absorption and transmission spectra, determination of the total molecular column and altitude profiles of molecular concentrations, radiative transfer in the atmosphere, radiation blocks of climate models, etc.
The use of simplified models is due to the fact that there is no empirical information about many dark vibrational states and their parameters cannot be estimated with sufficient accuracy. These circumstances lead to deterioration in the quality of the description (an increase of RMS deviations). A particular case of a very highly excited state assigned as (1. 6. 3) was discussed in  [33] ; the largest value of the corresponding RMS deviation ~0. 075 cm -1 is due to the issues of the applicability of the conventional EH model in this energy range  [32]. One of the ways to obtain more accurate values of line positions in databases is to replace the calculated transition frequencies with observed values (or with the difference in empirical energy levels obtained from the observed line positions) when the differences will be greater than some chosen value (for example 0.
001 cm -1 ). In a recent paper  [21] , this was done for the S&MPO database  [64]  and will be integrated in the two other databanks  [24, 223]. Note that these changes correspond to long and tedious work, since the same change must be applied to all transitions of the same upper energy level. This corresponds to three transitions in the A-type band and six in the B-type band. In addition, this change should also be made for hot bands, in particular, having the (010), (001), (100), and (020) states as lower ones. The statistics of these changes made for the S&MPO database are summarized in Figure  12 , as given in  [21]. Corrected (ν corr ) and uncorrected (ν un- corr ) line positions correspond to the SMPO2020 and SMPO2017 line lists, respectively. A particular case of a very highly excited state assigned as (1.
Recent Results One of the ways to obtain more accurate values of line positions in databases is to replace the calculated transition frequencies with observed values (or with the difference in empirical energy levels obtained from the observed line positions) when the differences will be greater than some chosen value (for example 0. 001 cm -1 ). In a recent paper  [21] , this was done for the S&MPO database  [64]  and will be integrated in the two other databanks  [24, 223]. Note that these changes correspond to long and tedious work, since the same change must be applied to all transitions of the same upper energy level. This corresponds to three transitions in the A-type band and six in the B-type band. In addition, this change should also be made for hot bands, in particular, having the (010), (001),  (100) , and (020) states as lower ones.