dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgments: We thank  Andrejs Kostromins ,  Thomas Pfau , and  Ronan M. T. Fleming , as well as other members of the  COBRA Toolbox google forum , for their help in the use of the Toolbox. We also thank  Jared Broddrick ,  Nicolas Schiffrin ,  Dany Croteau ,  Manish Kumar , and  John A Raven  for helpful discussions.
The molecular jet Fourier-transform microwave spectrum of 4,5-dimethylthiazole has been recorded between 2. 0 and 26. 5 GHz, revealing torsional splittings arising from two inequivalent methyl internal rotations with relatively low hindering barriers and nitrogen quadrupole hyperfine structures. Two global fits with 1009 hyperfine components of 315 rotational transitions involving five torsional species were performed using the program XIAM and BELGI-Cs-2Tops-hyperfine, an extended version of the BELGI-Cs-2Tops code which includes the effect of the 14 N quadrupole coupling, giving a root-mean-square deviation of 399. 8 kHz and 4. 2 kHz, respectively. Compared to the monomethyl substituted thiazole derivatives, the barriers to internal rotation are drastically lower. This is also in contrast to chemical intuition which suggests high barriers due to steric hindrance.
However, spectra of molecules with low barriers to internal rotation often cannot be modeled correctly with XIAM due to the limited number of fit parameters  [13] [14] [15]. Implementing higher order terms in the program is a difficult task. The disadvantages of the XIAM code in dealing with low barriers to internal rotation can be overcome with the BELGI-Cs-2Tops program, which succeeded to fit the microwave spectra of molecules with Cs symmetry and two methyl tops to experimental accuracy, e. g. methyl acetate  [16] , ethyl methyl ketone  [17] , and dimethylbenzaldehyde  [18] , by adding higher order terms in the Hamiltonian  [19]. However, BELGI-Cs-2Tops does not include the quadrupole coupling effect. Therefore, we decided to extend the program to a BELGI-Cs-2Tops-hyperfine version to treat the microwave spectrum of 45DMTA by taking into account the effect of weak nuclear quadrupole coupling using a first order perturbation approximation.
Geometry optimizations As other thiazole rings, 45DMTA is planar and aromatic because of the π electron delocalization of the two conjugated double bonds. This constraint confines the structural analysis to have only one starting geometry. Full geometry optimizations were performed on this initial forms using the B3LYP, M06-2X, MP2, and CCSD methods in combination with various Pople and Dunning basis sets  [20, 21]  as implemented in the GAUSSIAN09 package  [22]. The geometry optimized at the MP2/6-311++G(d,p) level of theory is shown in Figure  2  in the principal axes of inertia. The nuclear Cartesian coordinates are given in Table  S -1 in the Supplementary Material. Harmonic frequency calculations were carried out to verify whether the stationary point is a saddle point or a true minimum geometry.
The BELGI-Cs-2Tops-hyperfine code The BELGI-Cs-2Tops program has been slightly modified to treat hyperfine splittings in the rotational spectrum arising from weak nuclear quadrupole coupling of the nitrogen atom. A perturbation approach has been applied, which is similar to that used first for acetamide (see Eq. 1 of Ref. [30] ), then for N-tert-butylacetamide (see Eq. 1 of Ref. [31] ). The molecular symmetry is Cs in all cases, only the number of rotors increases to two in the present case. In BELGI-Cs-2Tops-hyperfine, like in the BELGI-Cs-2Tops code  [19] , we follow the Hamiltonian initially described by Ohashi et al  [32]. The Hamiltonian is set up using a modified Principal Axis Method (PAM) in which the coefficients of the three quadratic rotational operators (PxPy + PyPx), (PyPz + PzPy), and (PzPx + PxPz) are kept fixed to zero in the fit (see Eq.
(  6 ) of Ref. [32] ). We will refer to it hereafter as the Ohashi-Hougen Hamiltonian. In this Hamiltonian, the nuclear quadrupole interaction terms were also included, taken from the usual form (e. g. Eq. (  1 ) of  [30] ). However, the BELGI-Cs-2Tops-hyperfine code differs from that in Ref. [32]  because it solves the torsion-rotation Hamiltonian in a two-step diagonalization procedure  [33] , where the first step deals with the torsion-K-rotation part of the problem, and the second step deals with all the rest. This procedure is explained in details in Eq. (3) of Ref. [19]  and in Eqs. (1)  and (2) of Ref. [18]. In the BELGI-Cs-2Tops-hyperfine code, the expectation values of various combinations of angular momentum components 〈 〉, 〈 〉, 〈 〉, and 〈 + 〉 are calculated. Subsequently, their numerical values are transferred into the standard hyperfine energy expression: ( , , = 2 ( , , ( +1 〈 〉 + 〈 〉 -( + 〈 〉 + 〈 + 〉 (1) where f (I, J, F) is the Casimir function  [34].
The shifts for each rotation-torsion energy level, and therefore those of the hyperfine components, can be calculated using Eq. (  1 ). This enables us to take into account all hyperfine patterns as well as to fit the rotational and rotation-torsional molecular parameters together with the nuclear quadrupole coupling constants in a global fit. The BELGI-Cs-2Topshyperfine code is currently available by one of the authors (I. K. ). In order to deduce physical meaning from the results of the fit, it is convenient to transform from the quasi-PAM parameters to PAM quantities. The details of the conversion program will be described in detail in section 2. 3 below.
Symmetry considerations G18 is the appropriate molecular symmetry group for 45DMTA which has a frame with Cs point-group symmetry and two inequivalent methyl groups  [36, 37]. There are different notations to describe the symmetry species of this group. In the Ohashi-Hougen code written to fit the microwave spectrum of N-methylacetamide  [32] , as well as in the BELGI-Cs-2Topshyperfine code, energy levels are labeled with A (=A1+A2), E1, E2, E3, and E4. Recently, another labeling scheme, for which the G18 group is written as the semi-direct product (8 o e ⊗8 o e ⨴ 8 q , has been introduced for 3,4-dimethylanisole  [38]  and then applied for 2,4dimethylanisole  [39]. Using this scheme, the torsional species can be labeled by the first part (σ1,σ2) of the full symmetry label given in Table  1  of Ref.
The program XIAM  [12]  was used to predict the torsional splittings. The initial values of the angles between the internal rotor axes and the principal axes of inertia as well as the hindering potentials were taken from ab initio calculation at the MP2/6-311++G(d,p) level of theory, those of the rotational constants, the centrifugal distortion constants, and the NQCCs from the rigid-rotor fit. The (01) and  (10)  species were assigned after a lot of trial and error, and we were able to get a satisfactory fit including the (00), (01), and (10) torsional species with their hyperfine components. However, we failed to assigned any (  11 ) and (  12 ) species with the prediction using molecular parameters from this fit. In figure  6 , a portion of the broadband spectrum with the 404 ← 313 and 414 ← 303 rotational transitions is given as an example.
Therefore, the U values of both methyl groups were fixed to the calculated values, which correspond to dU values of 160 GHz. Using the same data set the BELGI-Cs-2Tops-hyperfine code floated 37 parameters, which are the three rotational constants A, B, C, five quartic centrifugal distortion constants, the NQCCs χaa, χbb, and χab in Eq. (  1 ), the r1 and r2 parameters multiplying the off-diagonal ) + and ) + , terms, respectively, the potential barrier heights for each top V31 and V32, the rotation-torsion coupling term q1 and q2 (which are related to the ρ1 and ρ2 constants). Fifteen higher order terms were also determined representing the rotation-torsion interaction beyond the rigid top-rigid frame model, and finally five terms corresponding to the top-top interaction (V12cc, V12ss, F12, B12, r12P).
Quality of the fits The fit given as Fit XIAM in Table  2  has an rms deviation of 399. 8 kHz, which is 100 times the estimated measurement accuracy of 4. 0 kHz. This can be explained by the relatively low hindering potentials of both methyl groups and the rather significant coupling between the two tops. Similar deviations have been found in many one-top problems with similar barrier heights treated by the program XIAM, i. a. ethyl acetate (101. 606(23) cm -1 , 85. 3 kHz)  [42] , allyl acetate (98. 093(12) cm -1 , 54. 0 kHz)  [43] , and vinyl acetate (151. 492(34) cm -1 , 92. 3 kHz)  [44]. If top-top coupling is present, as in the case of pinacolone, the rms deviation determined by XIAM is even worse (121. 532(57) cm -1 , 1155. 8 kHz)  [45]. We notice that the rms value can be reduced from 399.
Acknowledgments We thank  Dr. Alexandra Welzel  for the results from her Ph. D. thesis entitled " Bau einer heizbaren Ultraschalldüse zur mikrowellenspektroskopischen Untersuchung schwerflüchtiger Substanzen im Molekularstrahl " at the  RWTH Aachen University. V. V. thanks the  Fonds der Chemischen Industrie (FCI)  and T. N. the  Université de Paris  for a Ph. D. fellowship. Simulations were performed with computing resources granted by  JARA-HPC  from the  RWTH Aachen University  under the project  jara0124. This work is supported by the  Agence Nationale de la Recherche ANR  (project  ID   ANR-18-CE29-0011 ). 28.
Large observational clinical datasets become increasingly available for mining associations between various disease traits and administered therapy. These datasets can be considered as representations of the landscape of all possible disease conditions, in which a concrete pathology develops through a number of stereotypical routes, characterized by 'points of no return' and 'final states' (such as lethal or recovery states). Extracting this information directly from the data remains challenging, especially in the case of synchronic (with a short-term follow up) observations. Here we suggest a semi-supervised methodology for the analysis of large clinical datasets, characterized by mixed data types and missing values, through modeling the geometrical data structure as a bouquet of bifurcating clinical trajectories.
The methodology is based on application of elastic principal graphs which can address simultaneously the tasks of dimensionality reduction, data visualization, clustering, feature selection and quantifying the geodesic distances (pseudotime) in partially ordered sequences of observations. The methodology allows positioning a patient on a particular clinical trajectory (pathological scenario) and characterizing the degree of progression along it with a qualitative estimate of the uncertainty of the prognosis. Overall, our pseudo-time quantification-based approach gives a possibility to apply the methods developed for dynamical disease phenotyping and illness trajectory analysis (diachronic data analysis) to synchronic observational data. We developed a tool ClinTrajan for clinical trajectory analysis implemented in Python programming language.
Background Large observational datasets are becoming increasingly available, reflecting physiological state of observed individuals, their lifestyles, exposure to environmental factors, received treatments and passed medical exams. From the big data point of view, each person's life can be represented as a trajectory in a multidimensional space of qualitative or quantitative traits. Simultaneous analysis of a large number of such trajectories can reveal the most informative features whose dynamics is correlated with trajectory clusters, associations between various factors and, potentially, the "points of no return", i. e. bifurcations representing important fate decisions. The most important applications of such a framework are medical. The notion of "disease trajectory" as a person's trajectory in the data space of various diagnoses (diseases quantified by their severity) accompanying the person's life has emerged recently and became available for the large-scale analyses in certain contexts  [ , ].
For example, a dataset containing an electronic health registry collecting during years and covering the whole population of Denmark, with. million individuals, have been analyzed with an objective to determine previously unreported disease co-morbidities [ ]. An ambitious 'Data Health Hub' (https: //www. health-data-hub. fr/) project has been recently launched in France with the aim to make available for machine learningbased analysis the collection of several decades-long populationwide anonymized health insurance records [ ]. A formal review and meta-analysis of scientific texts using the concept of patient trajectory (or clinical pathway) based on disease management and care but also considering medico-economic aspects with a focus • Large-scale observational clinical datasets represent landscapes of the variety of disease states • Diachronic clinical trajectories can be approximated from the multi-dimensional geometry of synchronic data and used for disease dynamical phenotyping • ClinTrajan: Python package for finding and analyzing clinical trajectories using elastic principal graph method on myocardial infarction has been recently published in [ ].
However, examples of massive comprehensive and life-long longitudinal clinical data are still rare. Most of the existing clinical datasets correspond to relatively short periods of patients' stays inside hospitals, or during their treatment for a particular disease. In this sense, clinical datasets frequently represent detailed but rather "static snapshot" than the dynamical picture of the individuals' states. Nevertheless, one can hypothsize that such a snapshot, if sufficiently large, can sample the whole landscape of possible clinical states with certain routes and branches corresponding to some averaged illness trajectories. Then each patient can be thought to occupy a particular position along such a trajectory, where those patients following the same trajectory can be ranked accordingly to the progression along it from the hypothetical least heavy state towards some extreme state.
Many of these methods are able to detect branching trajectories, where the branches can represent important bifurcations (or, cell fate decisions) in the dynamical molecular processes underlying differentiation of developmental programs. The aim of the present study is to suggest and test a computational methodology for extracting clinical trajectories from sufficiently large synchronic clinical datasets. Clinical trajectory is a clinically relevant sequence of ordered patient phenotypes representing consecutive states of a developing disease and leading to some final state (i. e. , a lethal outcome). Importantly, in our approach we do not assume that these are the same patient's states, even if this can be so in the case when there exist some longitudinal observations. Each clinical trajectory can be characterized by its proper pseudotime which allows one to quantitatively charac-terize the degree of progression along the trajectory.
Each clinical variable can be analyzed as a function of pseudotime conditioned on a given clinical trajectory. We also assume that clinical trajectories can be characterized by branches (bifurcations), representing important decisive moments in the course of a disease. An important methodological difference between the previously developed methodology of cell trajectory analysis in omics datasets, where the majority of the variables can be considered continuous and of similar nature (e. g. , gene expression levels), the clinical datasets possess certain specifics which must be taken into account. Typical real-life clinical data are characterized by the following features: a) they contain mixed data types (continuous, binary, ordinal, categorical variables, censored data); b) they typically contain missing values with non-uniform missingness pattern across the data matrix; c) they do not have a uniquely defined labeling (part of the clinical variables can be used to define clinical groups, but this can be done in several meaningful ways).
This means that an important integral part of the methodology should be procedures for quantifying and imputing missing values in mixed type datasets making them amenable for further application of machine learning methods. The last feature (c) suggests that unsupervised or semi-supervised methodology might play more important and insightful role here than purely supervised methods. We develop a methodology of clinical data analysis, based on modeling the multi-dimensional geometry of a clinical dataset as a "bouquet" of diverging clinical trajectories, starting from one or several quasi-normal (least severe) clinical states. As a concrete approach we exploit the methodology of elastic principal trees (EPT), which is a non-linear generalization of Principal Component Analysis (PCA). Principal tree is a set of principal curves assembled in a tree-like structure, characterized by branching topology  [ , ].
Principal trees can be constructed using ElPi-Graph computational tool, which has been previously exploited in determining branching trajectories in various genomics datasets (in particular, in single cell omics data)  [ , ,  ]. As an unsupervised machine learning method, estimating elastic principal graphs solves several tasks simultaneously, namely dimensionality reduction, data visualization, partitioning the data by the nonbranching graph segments (analogous to clustering) and quantifying robust geodesic distances (pseudo-times) from one data point to another along the reconstructed principal graph. Unlike many other methods relying on heuristics for guessing the optimal graph topology (e. g. , a tree) such as Minimal Spanning Tree (MST), elastic principal graph method optimizes the graph structure via application of topological grammars and gradient descentlike optimization in the discrete space of achievable graph structures (e.
g. , all possible tree-like graphs)[ ]. The suggested method is implemented as Python package, ClinTrajan, which can be easily used in the analysis of clinical datasets. We provide several reproducible Jupyter notebooks illustrating the different steps of the methodology. The figures in this paper are directly copied from these notebooks. The methodology proved to be scalable to the datasets containing hundreds of thousands of clinical observations, using an ordinary laptop, and can be scaled up further for even larger datasets.
Complications of myocardial infarction database Myocardial infarction (MI) is one of the most dangerous diseases. The wide spread of this disease over the past half century has made it one of the most acute problems of modern medicine. The incidence of myocardial infarction (MI) remains high in all countries. This is especially true of the urban population of highly developed countries, exposed to the chronic effects of stress factors, irregular and not always balanced nutrition. In the United States annually, more than one million people become ill with myocardial infarction [ ]. The course of the disease in patients with MI is diverse. MI can occur without complications or with complications that do not worsen the long-term prognosis. At the same time, about half of patients in the acute and subacute periods have complications leading to a worsening of the course of the disease and even death.
Even an expert can not always foresee the development of these complications. In this regard, predicting the complications of myocardial infarction in order to timely carry out the necessary preventive measures seems to be an important task. The database analyzed here was collected in the Krasnoyarsk Interdistrict Clinical Hospital (Russia) in -years, but has only recently been deposited to the public domain. The original database and its description can be downloaded from [ ]. It contains information about patients characterized by features describing the clinical phenotypes and features representing possible complications of the myocardial infarction disease ( features in total). Previously, the dataset was a subject of machine learning method applications, including convolutional neural networks [ ] and dimensionality reduction methods [ ].
Diabetes readmission data set Together with myocardial infarction, various diabetes-related clinical states such as hyperglycemia are widely spread in the modern population. The management of hyperglycemia in the hospitalized patients has a significant bearing on outcome, in terms of both morbidity and mortality [ ]. An assembly and analysis of a large clinical database was undertaken to examine historical patterns of diabetes care in patients admitted to a US hospital and to inform future directions which might lead to improvements in patient safety [ ]. In particular, the use of HbA c as a marker of attention to diabetes care in a large number of individuals identified as having a diagnosis of diabetes mellitus was analyzed. A focus was on the readmission probability of a patient after leaving the hospital and its dependency on other clinical features that can be collected during hospitalization.
Analyses ClinTrajan package for trajectory inference in large clinical datasets We suggest computational methodology of constructing principal trees in order to extract clinical trajectories from large-scale clinical datasets which takes into account their specificity. The following steps of the analysis have been implemented: • Univariate and multi-variate quantification of nominal variables, including an original implementation of the optimal scaling procedure for ordinal values • Several methods for missing values imputation including two original implementations of SVD-based imputers • Constructing principal tree for a quantified clinical dataset • Partitioning the data accordingly to the non-branching segments of the principal tree (analogue of clustering) and associating the segments to clinical variables • Extracting clinical trajectories and associating the trajectories to clinical variables • Visualization of clinical variables using principal trees and metro map data layouts [ ] • Pseudotime plots of clinical variables along clinical trajectories, visualization of their bifurcations.
Quantification of nominal values and imputation of missing data values As a first step of pre-processing, variables have been removed from the initial myocardial infarction complication data We considered that the small number of continuous numerical variables is not enough to apply the methodology of Categorical Principal Component Analysis (CatPCA) [ ]. Therefore, for all ordinal and binary variables we first applied the univariate quantification following the approach described in the 'Methods' section. This quantification allowed applying 'SVDComplete' imputation method for imputing the missing values, as described in 'Methods'. After all missing values have been imputed, we could apply the optimal scaling approach for ordinal values, optimizing the pairwise correlations between them and between ordinal and continuous numerical variables.
Constructing elastic principal tree The initial data space was formed by variables. We evaluated the global intrinsic dimension of the dataset using several methods implemented in https://github. com/j-bac/scikit-dimension, plementary Figure ). We compared the estimations of intrinsic dimensions with and without complication variables and found them to be similar, which indicates that there exists a certain level of dependency between the complication variables and the rest of the clinical variables. We also observed that the screen plot for this dataset is characterized by elbow approximately at n =. As a result of this analysis, for further inference of the principal tree, we projected the dataset into the space of the first principal components. The elastic principal tree was computed using ElPiGraph Python implementation as documented in the Jupyter notebook provided at https://github.