dataesr/scientific-paragraphs-categorization huggingface dataset:
Progressive Three-State Model for the Stanford Heart Transplant data As an illustrative example, we revisit the analysis of the Stanford Heart Transplant data, freely available through the survival package. A full description of the data can be found in  [20]. The dataset presents the survival of patients on the waiting list for the Stanford heart transplant program. We analyze the data similarly to  [38]  which use their R package p3state and propose an illness-death model similar to Figure  2. Their states represent "alive without transplant", "alive with transplant", and "dead". We consider the same dataset, where patients' records from October 1967 (start of the program) until April 1974 includes the information of 103 patients where 69 received heart transplants, and 75 died. Three fixed covariates for each patient are available.
These include the age at acceptance (age), the year of acceptance (year), and previous surgery (surgery: coded as 1 = yes; 0 = no). We first use the data without taking into account any covariate effects to show that an exponential distribution on the baseline hazard rate of the sojourn time, α ij (•) does not produce constant intensity transition functions, αij (•). This point was shown theoretically in Example 2, of Section 2. 4 and we now illustrate it using data and the SemiMarkov package. Using the package we obtain both α ij (•) and αij (•) for (i, j) = (1, 2) and (i, j) = (1, 3). The results are in Figure  4  where we see that while α ij (•) are constant, αij (•) are clearly not constant across time. These curves in fact follow a form like  (19). We now continue to analyze the data fully with Approach I using the SemiMarkov package where we compare different parametric forms and covariates in the model.
For choosing between the different proposed models, we use the Expected Kullbak-Leibler (EKL) risk as in  [35]. This is done via the Akaike Information Criterion (AIC) which is an estimate of the EKL risk in a parametric framework using maximum likelihood method, see  [34, 18]. For each of the 6 models described above, we obtain the AIC using output from SemiMarkov and present it in the first part of Table  2. The best model according to the AIC is given by the Exponentiated Weibull model. However, due to convergence issues during the optimization (see the vignette  [33] ), we select the second best result given by the Weibull/Exp + Select model as the most appropriate model for this dataset according to AIC using Approach I. Moving onto inference using Approach II, we investigate and estimate different models by specifying different proportional intensity transition models as defined in equation  (33).
We use flexsurv to estimate αij (•) for several models which we present in the second part of Table  2. The models Expo-nential, Weibull, Gamma, and Generalized Gamma are all estimated with all three covariates in the model. The additional two models, Weibull+Select, and Generalized Gamma + Select, have a reduced set of covariates with a procedure consistent with that used for Approach I above. More details are in the vignette (see  [33] ). The AIC based performance of each of these models is presented in the second part of Table  2. The best model according to the AIC is Generalized Gamma + select. In this model only the age covariate is used for transition 1 → 2, only the year covariate is used for transition 1 → 3, and both the surgery and age covariates are used for transition 2 → 3. For this dataset, the best model based on Approach I presents a better AIC value (1639.
Reversible Semi-Markov Model for the Asthma Control Data We revisit the analysis of the asthma control data which has been used to illustrate the SemiMarkov R package in  [31]. See also the related papers using the same data,  [44]  and  [45]. The data consists of the follow-up of severe asthmatic patients consulting at varied times according to their perceived needs. At each visit, several covariates were recorded and asthma was evaluated. The available data (asthma) from the SemiMarkov package presents a random selection of the 371 patients with at least two visits. In this illustration, we only use the BMI (Body Mass Index) covariate coded: 1 if BMI ≥ 25 and 0 otherwise. Similarly to the analysis in  [31] , we use a reversible three-state model as presented in Figure  6. This investigates the evolution of asthma based on, "optimal control" (State 1), "sub-optimal control" (State 2) and "unacceptable control" (State 3).
Then one identifies adjacent faces so that the orientation on the edges match [7, Fig. 1 ]. The resulting hyperbolic manifold has minimal volume among non-compact hyperbolic manifolds. This volume is Gieseking's constant Q(i √ 3)  [14, 15]. The fundamental group for the Gieseking manifold is denoted m000 in SnapPy software  [17]. The fundamental group is π 1 (m000) := x, y|x 2 y 2 = yx. The cardinality sequence η d (π 1 (m000)) of subgroups of index d < 15 of π 1 (m000) is given in Table  2. The permutation groups organizing the cosets of subgroups of π 1 (m000) up to index 10 are in Table  1. The identification of submanifolds follows from SnapPy. In the next section, we find that a model of the secondary structure in histone H3 (PDB 6PWE 1) (obtained with the software PORTER) is the group G := C, H|C 44 H 12 C 4 H 3 C 3 H 12 C 8 H 28 C 7 H 10 C 5.
0  [19] , PORTER 4. 0  [20] , PHYRE2  [21]  and RAPTORX  [22]. We do not enter into the details about the theory of these softwares. Below, we we find that PORTER 4. 0 is often well adapted to our goal of identifying an algebraic secondary structure. PORTER 4. 0 uses two cascaded bidirectional recurrent neural networks: one for prediction and one for filtering. The method has been trained and benchmarked by cross-validation on a set of many non redundant proteins. 3. 1. The primary (linear) structure. The mRNA sequence for histone H3 of drosophila melanogaster may be found in  [23]  with the reference NM 001032216. 2. It contains 529 base pairings (529 bp). A convenient way to pass from the NCBI format (with line feeds, numbers and blank spaces) to the bare linear sequence is to make use of a software such as Massager  [24].
In the protein data bank the gamma-carbonic anhydrase for methanosarcina thermophila (PDB 1QRE 1) is a sequence with 247 aa. As for myelin P2, using Table  3 , one observes that the cardinality sequence of subgroups in the PHYRE2 and PORTER models of the secondary structure of 1QRE 1 corresponds to that of the cartographic group C 2 up to index 4. The complex is 3-fold symmetric as shown in Fig. 3a.
4. 4. Other n-fold symmetric complexes. The 5-fold symmetric H2A-H2B complex in nucleoplasmin (PDB 2XQL). Molecular chaperones are proteins that help the folding or unfolding and the disassembly of other molecular structures. Nucleoplasmin, the first identified molecular chaperone, promotes the in vitro assembly of nucleosomes. The latter are the topic of our next section. There is a histone octamer comprising two H2A-H2B dimers and an H3-H4 tetramer. The H2A-H2B histone complex is investigated in  [26]. It has a pentameric structure as shown in Fig. 4a  and is referred as 2XQL in the protein data bank. We performed an investigation of the secondary structure of the 2XQL 1 protein that one finds in each of the 5 arms of the complex. PSIPRED and PORTER models predict a secondary structure with α helices and coils only that we could not compare to a known group theoretical sequence.
The PHYRE2 and RAPTORX models, as well as our approach based on the mapping of aminoacids to the characters of group G 7 and G 8 (explained below), predict a cardinality sequence which fits that of the cartographic group C 2 , as shown in Table  3. The 5-fold symmetric acetylcholine receptor (PDB 2BG9). The acetylcholine receptor is an integral membrane protein that responds to the binding of the acetylcholine neurotransmitter. This receptor is also sensitive to nicotine and muscarine. It has a pentameric structure shown in Fig. 4b  and is refereed as 2BG9 in the protein data bank. We performed an investigation of the secondary structure of the 2BG9 1 protein that one finds in the 5 arms of the complex. As shown in Table  3 , all models predict a secondary structure with α helices, β sheets and coils.
We can refine the technique by introducing more structure in the pseudo coil segments. Some of the slots/amino acids correspond to a character with constant entries and we choose to encode them as C 0 as before and the remaining slots/amino acids which correspond to a non constant entry (z 1 or z 1,3 ) are encoded with E 0 , that we consider as a pseudo-sheet. Then we can define the group G 0 := H 0 , E 0 , C 0 |rel(H 0 , E 0 , C 0 ) , where rel(H 0 , E 0 , C 0 ) is the new model of the protein secondary structure obtained by our definition of pseudohelices H 0 , pseudo-sheets E 0 and pseudo-coils C 0. In table 3, the cardinality structure of group G 0 is compared to that of the other models PSIPRED, PHYRE2, PORTER and RAPTORX. One finds that the cardinality sequence either fits, at the first few places, the cartographic group C 2 or that of a 3-manifold.
It leaves open the question whether one of the standard models or our own model is the most efficient. 5. The 8-fold symmetric histone complex of the nucleosome: 3WKJ in the protein data bank Strong DNA packaging is found in the nucleosome of eukaryotes. The nucleosome complex consists of a double helix wrapped around a set of eight histone proteins comprising two copies of H2A, H2B, H3 and H4. The nucleosome is the fundamental subunit of chromatin. Eukaryotic chromatin is further compacted by being folded into more complex structures eventually forming a chromosome. Nucleosomes are considered to be the support of epigenetic information. The nucleosome core particle contains approximately 146 base pairs (bp) of DNA wrapped in 1. 67 left-handed superhelical turns around the histone octamer as shown in Fig.
I. INTRODUCTION Model-based PHM approaches are mainly based on state observations in various engineering applications  [1]. The more the system is critical, the more the stability and accuracy constraints should be guaranteed. From the perspective of the high complexity level of the prognostics techniques, the PHM is directed towards complex uncertain systems with This work is partially funded by the Catalan Agency for Management of University and Research Grants (AGAUR) and the European Social Fund (ESF) of the Government of Catalonia through the grant FI-SDUR-AGAUR 2020 (ref. 2020-FISDU-307) and grant 001-P-001643 Agrupació Looming Factory. It is also partially funded by European Union and Normandy Region. Europe is involved in Normandy through the European Funds for Regional Development.
Main text While the SARS-CoV-2 Delta variant is now dominant worldwide, the emergence of the SARS-CoV-2 Omicron variant (B. 1. 1. 529) is causing global concern with its increasing spread. 1  However, whether the Omicron variant has a faster transmission and/or greater transmissibility in comparison with the Delta variant remains unclear. In the present study, we estimated serial interval and basic reproduction number (R 0 ), involved in the community transmission of the Omicron variant that was initiated from imported cases in South Korea. We collected publicly available data of the case of the Omicron variant from the Korean public health authorities. 2, 3   o identify the Omicron variant, public health authorities conducted whole-genome sequencing from respiratory samples from the epidemiologically linked individuals with the omicron variant who tested positive for SARS-CoV-2 by RT-PCR.
The Omicron variant case included occurred during November 25, 2021 -December 16, 2021, when the community transmission that was initiated from imported cases reported from the Korea Disease Control and Prevention Agency. The data included contact tracing with other reported cases of the Omicron variant and demographic characteristics of the cases, including age, date of symptom onset, source of infection. We computed the serial interval as the number of days between the infector and that of the infectee in the transmission pairs. Furthermore, we estimated the serial interval distribution by fitting a normal distribution. 4 r the newly emerging infectious diseases, the number of cases increases exponentially in the initial phase of an outbreak. The observed value of the exponential growth rate (r) is often related to the basic reproductive number, R 0.
The python code used for our simulations  [22]  is modular and comparisons with other inference procedures can be performed by adding new modules. Scheme of propagation A convincing validation of any individual-level intervention policy requires extensive simulations by means of sufficiently detailed agent-based models. In such models, at each time, a given individual is in a state that belongs to a finite set of possible states, like for instance susceptible, exposed, infected-asymptomatic, infected-asymptomatic, in ICU, recovered, or dead. The most accurate mathematical descriptions of COVID-19 epidemic propagation are based on complex multi-state compartment models, in which infected individuals are not immediately contagious upon infection, may be asymptomatic or develop mild/severe symptoms with some delay, and the ages, households and workplaces are also taken into account.
Acknowledgments We would like to thank the  ELLIS network  for organizing a series of COVID-19 related workshops. We also want to thank  Yoshua Bengio ,  Irina Rish , the MILA team working on the contact tracing problem, as well as  Luca Ferretti  and  Ivan Bestvina  for numerous enlightening discussions. We acknowledge computational resources provided by  HPC@POLITO  (http://www. hpc. polito. it)and well as  Google Cloud  for the SIPAR grant in  COVID-19 research credits program. This work has been partially supported by the  SmartData@PoliTO  (http://smartdata. polito. it)center on Big Data and Data Science, the  French Agence Nationale de la Recherche  under grant  ANR-17-CE23-0023-01 PAIL  and from the Chaire CFM-ENS on data science.
Structure of the manuscript The manuscript is organized as follows. In Section 2 the abstract pHs framework is introduced, with a particular focus on both hyperbolic and parabolic linear systems of partial differential equations. In Section 3 the general structure-preserving discretization is presented, and then specialized on the two cases previously mentioned. In Section 4 the ongoing environment SCRIMP is described in detail. In Section 5 the three companion interactive Jupyter notebooks  [6]  are thoroughly explained. Conclusions and perspectives are finally drawn in Section 6.
The Partitioned Finite Element Method (PFEM) We are now in a position to introduce a general methodology to discretize infinite-dimensional pHs in a structure-preserving manner. The main contribution in this section is the application of PFEM to a general abstract class of pHs, unifying the previously published results. This generality is notably of particular interest for the development of a well-structured software for the numerical simulations of physics-based models. The power balances  (14) ,  (20)  are deeply linked to a linear underlying Stokes-Dirac. The main idea of PFEM is to mimic this structure, in order to obtain a discretized copy of these power balances as  (2). This systematically translates the Stokes-Dirac structure into a finite-dimensional Dirac structure. The compatible discretization, with respect to this Dirac structure, of the constitutive relations allows to mimic the continuous power-balance.
As already mentioned, dissipation (both in the domain and on the boundary) can also be considered in this strategy  [30]   [31]. Hence a very wide class of (nonlinear) multiphysics systems can be discretized in a structure-preserving manner (with well-represented exchanges of energy between the subsystems). In the next section we present an ongoing project which has been initiated to prove the efficiency of the PFEM methodology, leveraging well-established and robust software tools for the finite element discretization of partial differential equations and time integration.
SCRIMP: Simulation and Control of Interactions in Multi-Physics In this section the main features related to the numerical simulation of pHs in the framework of the ongoing project named SCRIMP (Simulation and Control of Interactions in Multi-Physics) are detailed. The aim is to provide a flexible prototype Python code for the numerical simulation of pHs both for research and educational purposes. In addition to numerical experiments proposed later in Section 5, the reader is referred to interactive companion Jupyter notebooks  [6]  to learn how to numerically solve the model problems introduced in Section 3 with SCRIMP. In the following, the key ideas behind SCRIMP are mentioned and then a specific emphasis on both space and time discretizations is given. A.
Key Ideas Behind SCRIMP In short, the key ideas related to the design of SCRIMP are provided: • The Python dynamic programming language has been selected due to its expressiveness and the availability of high-level interfaces to scientific computing software libraries  [43] ; • SCRIMP assumes to rely on open-source, external software for the finitedimensional discretization of partial differential equations; • SCRIMP encapsulates the finite-dimensional objects related to the finite element discretization in space (e. g. matrices) to deduce the resulting linear or nonlinear pHs in a generic pHODE/pHDAE form as proposed in  [26] ; • For multiphysics problems, this design offers the advantage that discretization in space may be handled by different software components depending on the discipline or on the modelling.
The modularity and the object-oriented nature of Python thus offer the flexibility to easily combine the different pHs to deduce the global interconnected system. This is much in line with the mathematical theory of pHs  [24]. Furthermore we note that interconnections of different systems (with e. g. the transformer or gyrator transformations  [24] ) can be easily incorporated. The design of SCRIMP is based on procedural and object-oriented paradigms and thus follows the standard ideas governing most of the numerical PDE software. Whereas a detailed exposition of the design patterns of SCRIMP and its performance will be published elsewhere, concrete illustrations of most of these key ideas can be found in the companion Jupyter notebooks  [6]. The description of the current numerical methods related to space and time discretizations available in SCRIMP is given.
Semi-Discretization in Space As outlined in Section 3, PFEM relies on an abstract variational formulation written in appropriate finite element spaces. To perform the semi-discretization in space, we rely on FEniCS  [23] , an open-source C++ scientific software library that provides a high-level Python interface. The FEniCS Project is mainly based on a collection of software components targeting the automated solution of partial differential equations via the finite element method. Its core components notably include the Unified Form Language (UFL)  [44] , the FEniCS Form Compiler (FFC)  [45]  and the finite element library DOLFIN  [46] , which contains various types of conforming finite element methods, e. g. , nodal Lagrangian finite elements for grad-conforming approximations or non non-nodal finite elements (e.
g. , Raviart-Thomas spaces for div-conforming approximations) as well. These families of finite elements are notably required to tackle the discretization in space of our core problems. A key point to facilitate the generic implementation of PFEM is the use of UFL. UFL is indeed an expressive domain-specific language for abstractly representing (finite element) variational formulations of differential equations. In par- ticular, this language defines a syntax for the integration of variational forms over various domains. This simply leads to an expressive implementation that is close to the abstract mathematical formulations presented in Section 3. The FEniCS Form Compiler FFC then generates specialized C++ code from the symbolic UFL representation of variational forms and finite element spaces.
We note that setting the initial conditions properly is of utmost importance for a DAE solver. To do so, we rely on To the best of our knowledge, open-source libraries for the solution of general nonlinear differential algebraic equations with high-level Python interfaces are not yet available. Hence a simple forward in time integration method for the solution of the nonlinear pHDAE related to the energy formulation of the heat equation problem has been provided; see  [51]  for illustrations and discussion. As a future direction, we plan to investigate the potential of the PETSc's time stepping library TS  [52]  to be able to tackle the solution of large-scale pHDAE systems.
FEniCS Expressions Definition For the finite element discretization of the pHs, the FEniCS library is used in the Wave_2D class of SCRIMP. Hence to properly use FEniCS expression definition, we provide the definition of the different variables in C++ code given in strings. We first specify the mass density as a function depending on the space coordinates. Hence in this expression, [ ] 0 x corresponds to the first spatial variable 1 0, 0, 0, , , 0, 0, , 0, , , 0, t t w t w w x t = = ∈ Ω = ∂ = ∂ = ∈ Ω = x x x x x x θ θ 0 0 (58) and boundary conditions: ( ) ( ) { } { } , 0, 0 , , 0,. , 0, D D N N D D N x y N Γ Γ Γ Γ = = Γ = = Γ = = = = ⋅ = ⋅ = q n M n θ (59) A.   = = -       π               = -    π      (60).
Acknowledgements This work is supported by the project  ANR-16-CE92-0028 , entitled Interconnected Infinite-Dimensional systems for Heterogeneous Media, INFIDHEM, fi- nanced by the  French National Research Agency (ANR)  and the  Deutsche Forschungsgemeinschaft (DFG). Further information is available at https://websites. isae-supaero. fr/infidhem/the-project. Moreover the authors would like to thank  Michel Salaün  and  Denis Matignon  for the fruitful and insightful discussions.
Acknowledgements We are grateful to  A. Kuznetsov  for a useful discussion, to  V. Kac  for sending us the paper [7], and to anonymous referees for correcting some inaccuracies and drawing our attention to [4]. V. G. has been partially supported by the  HSE University Basic Research Program ,  Russian Academic Excellence  Project  5-100 , and by the  RSF  Grant No. 20-61-46005.
BraMAH differs from other generic topological data analysis methods by its using explicitly the fact that the point cloud under study lies on a branched manifold, and by detecting relevant features such as branch torsions or weak boundaries, if they exist. In the presence of noise-driven chaos, the branched manifold is time-evolving and must therefore be analyzed time-wise, i. e. , using point clouds that approximate the random attractor by successive snapshots. The branched manifolds so constructed by BraMAH provide topological portraits at different stages in the life of LORA, the Lorenz model's random attractor. Our study shows a marked difference between the deterministic case and the noise-driven one. The stochastically perturbed system's random attractor, dubbed LORA, presents a much richer structure than the deterministic strange attractor, with a topology that also changes drastically in time.