Dr. Alberto Macario
email: alberto.macario@univ-rennes1.fr

Carlota Rodríguez

Juan Carlos López

Susana Blanco

Dr Garry Smitty Grubbs
email: grubbsg@mst.edu

Professor, Assocaite

Dr. Assimo Maris
email: assimo.maris@unibo.it

Prof Miller

Prof C Norman

Craig

THE CONFORMATIONAL LANDSCAPE OF α-AMINOGLYCINE

Keywords: microwave spectroscopy, computational chemistry, conformational analysis, amino acids, hydrogen bonding microwave spectroscopy, computational chemistry, conformational analysis, amino acids, hydrogen bonding

The conformational landscape of α-aminoglycine has been studied. A conformational search has been first done using a set of different low-cost computational methods. The conformers obtained have been finally optimized at MP2 and B3LYP-D3/6-311++G(2d,p) levels of theory. A conformational landscape of 15 conformers with relative energies lower than 2000 cm -1 has been obtained. For the global minimum (IIa) a cooperative network formed by an O-H•••N-H, NH•••N and N-H•••O=C hydrogen bonds, closing a sequential cycle stabilizes the structure. The next conformer in energy (Ia) also has two N-H•••O=C, and N-H••N and N-H•••O-H hydrogen bonds. The potential energy surfaces associated with different torsions have been investigated, to rationalize the stability of some conformers. The relative population ratio in a supersonic jet has been estimated to calculate the relative intensity of the rotational spectra of the predicted conformers.

Introduction

The molecular structure of the proteinogenic amino acids plays an important role in the secondary structure of proteins, that determines molecular recognition properties and their three-dimensional arrangement, and consequently governs the activity of proteins [1][START_REF] Barrett | Chemistry and Biochemistry of the Amino Acids[END_REF][START_REF] Barrett | Amino Acids and Peptides[END_REF]. Therefore, a great effort has been made in the last decades in order to investigate the molecular structure of proteinogenic -amino acids by means of high-resolution gas-phase microwave spectroscopy [START_REF] Alonso | Microwave spectroscopy of biomolecular building blocks[END_REF][START_REF] Suenram | Millimeter wave spectrum of glycine[END_REF][START_REF] Suenram | Millimeter wave spectrum of glycine. A new conformer[END_REF][START_REF] Godfrey | Shape of Glycine[END_REF][START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF][START_REF] Blanco | Revealing the multiple structures of serine[END_REF][START_REF] Blanco | Conformations of γ-Aminobutyric Acid (GABA): The Role of the n→π* Interaction[END_REF][START_REF] Lesarri | The Shape of Neutral Valine[END_REF][START_REF] Cocinero | The Shape of Leucine in the Gas Phase[END_REF][START_REF] Lesarri | Coded Amino Acids in Gas Phase: The Shape of Isoleucine[END_REF][START_REF] Alonso | Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study[END_REF][START_REF] Cocinero | Conformations of α-Aminobutyric Acid in the Gas Phase[END_REF][START_REF] Sanz | The Conformers of Phenylglycine[END_REF][START_REF] Pérez | Jet-Cooled Rotational Spectrum of Laser-Ablated Phenylalanine[END_REF]. However, most of amino acids present high melting points, low vapor pressures and low thermal stabilities which makes them to decompose upon heating being thus the gas phase spectrum not accessible by traditional vaporization methods. Thus, the study of the molecular structure of most amino acids [START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF][START_REF] Blanco | Revealing the multiple structures of serine[END_REF][START_REF] Blanco | Conformations of γ-Aminobutyric Acid (GABA): The Role of the n→π* Interaction[END_REF][START_REF] Lesarri | The Shape of Neutral Valine[END_REF][START_REF] Cocinero | The Shape of Leucine in the Gas Phase[END_REF][START_REF] Lesarri | Coded Amino Acids in Gas Phase: The Shape of Isoleucine[END_REF][START_REF] Alonso | Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study[END_REF][START_REF] Cocinero | Conformations of α-Aminobutyric Acid in the Gas Phase[END_REF][START_REF] Sanz | The Conformers of Phenylglycine[END_REF][START_REF] Pérez | Jet-Cooled Rotational Spectrum of Laser-Ablated Phenylalanine[END_REF] has been possible thanks to the use of laser ablation techniques coupled with high-resolution rotational spectroscopy [START_REF] Alonso | Microwave spectroscopy of biomolecular building blocks[END_REF][START_REF] Blanco | The structure of isolated thalidomide as reference for its chirality-dependent biological activity: a laser-ablation rotational study[END_REF]. On the other hand, prior to any experimental study it is necessary to develop a conformational search in order to analyze the intramolecular interactions involved, together with the conformational relative stability. Moreover, this allows to shed light on the possible interactions with other systems or solvents that could be present in their natural medium [START_REF] López | Conformational equilibria in o -anisic acid and its monohydrated complex: the prevalence of the trans -COOH form[END_REF][START_REF] Macario | Competition Between Intra-and Intermolecular Hydrogen Bonding: o -Anisic Acid⋅⋅⋅Formic Acid Heterodimer[END_REF][START_REF] Blanco | Structure and Dynamics in Formamide-(H2O)3: A Water Pentamer Analogue[END_REF][START_REF] Pinacho | Prediction of the rotational spectra of microsolvated complexes with low cost DFT methods[END_REF].

Glycine (Gly) is the simplest proteinogenic amino acid and the only one which is not chiral. Their molecular structure has been investigated by means of high-resolution molecular spectroscopy [START_REF] Suenram | Millimeter wave spectrum of glycine[END_REF][START_REF] Suenram | Millimeter wave spectrum of glycine. A new conformer[END_REF][START_REF] Godfrey | Shape of Glycine[END_REF]. Due to its small size, glycine plays an important role during chain compaction early in the secondary proteins structure folding, affecting the backbone flexibility and the formation of loops, turns, and helices of polypeptide chains [START_REF] Krieger | Effect of Proline and Glycine Residues on Dynamics and Barriers of Loop Formation in Polypeptide Chains[END_REF][START_REF] Jacob | The Role of Proline and Glycine in Determining the Backbone Flexibility of a Channel-Forming Peptide[END_REF]. Also because of its size, is the major participant in the formation of collagen triple-helix [START_REF] Berisio | Crystal structure of the collagen triple helix model [(Pro-Pro-Gly)(10)](3)[END_REF]. Being the simplest amino acid, their molecular structure has been taken as a model for the rest of amino acids. Ab initio computations predict several conformers but only two of them were observed in a supersonic jet [START_REF] Godfrey | Shape of Glycine[END_REF]. The most stable has an N-H•••O=C intramolecular hydrogen bond with the carboxylic group is in the most stable cis-COOH arrangement while the second conformer presents a O-H•••N intramolecular interaction with the acid group in a trans-COOH disposition. A third plausible conformer with an N-H•••O-H bond was reported to relax to the most stable form in the supersonic expansion.

Protein design and engineering is trying to expand the activity and functions of proteins [START_REF] Young | Beyond the canonical 20 amino acids: expanding the genetic lexicon[END_REF] by incorporating new amino acids beyond the natural ones and studying the molecular structure of these new species in order to reveal their chemical behavior [START_REF] López | Decoding the Structure of Non-Proteinogenic Amino Acids: The Rotational Spectrum of Jet-Cooled Laser-Ablated Thioproline[END_REF]. α-Aminoglycine (Agl) is one of such non-natural α-amino acids derived from glycine replacing one of its α hydrogen atoms by an amino group. The presence of two amino groups linked to the same carbon atom increases the number of possible intramolecular interactions, and consequently affects its conformational panorama, but also makes the system unstable. Therefore, its synthesis can only be achieved in its protected form [START_REF] Bock | Differentially protected .alpha.aminoglycine[END_REF]. Protected aminoglycine derivatives have been identified as useful scaffolds for the introduction of chemical diversity into bioactive polypeptides [START_REF] Far | Synthesis of glyoxylyl peptides using an Fmoc-protected α,α′diaminoacetic acid derivative[END_REF], for example in the formation of analogs of thyrotropin-releasing hormone (TRH) [START_REF] Kirby | Analogs of thyrotropin-releasing hormone using an aminoglycine-based template[END_REF]. It also presents anticonvulsant properties [START_REF] Kohn | Anticonvulsant Properties ofN-Substituted α,α-Diamino Acid Derivatives[END_REF]. Nevertheless, the chemical and biological properties associated to the molecular structure of Agl remain currently poorly understood.

The starting point of an experimental rotational spectroscopy study is the computational investigation of the conformational landscape. This search allows to understand how the molecule behaves as a subunit in other systems, such as in those in which it is in its protected form, and to unravel how interacts with itself and with other species. First, it is worth to characterize the intramolecular interactions which stabilize the molecule and unravel the large amplitude motions associated to its conformational groups which may provide the paths to interconvert and/or connect the different conformations. The conformational panorama also provides clues about the possible interactions with molecules in its environment, defining the functional groups affected by those interactions and the moyeties that could be unaltered by the media. This research allows also to determine or predict the possible intermolecular interactions of Agl with another species in isolation. In this work we aim to investigate the equilibrium structure and the conformational panorama of Agl.

Computational methods

In a first step of the conformational search of Agl, we employed the computational methods implemented in different programs [START_REF] Shao | Advances in methods and algorithms in a modern quantum chemistry program package[END_REF][START_REF] Frisch | Gaussian 16 Rev. C.01[END_REF]. These computational chemistry methods include molecular mechanics, semiempirical, ab initio and DFT. In a second step for each predicted conformer a geometry optimization was done employing Gaussian G16 [START_REF] Frisch | Gaussian 16 Rev. C.01[END_REF] at ab initio MP2/6-311++G(2d,p) and DFT B3LYP-D3/6-311++G(2d,p) levels of theory. This has allowed us to obtain the equilibrium structure for each conformer and to calculate the different spectroscopic parameters needed to predict the rotational spectra. Complementary vibrational frequency calculations were also done in order to ensure that the predicted conformers are true minima and to evaluate Gibss energies.

Molecular mechanics are based on classic mechanics concepts and considers the molecule as a matrix of atoms governed by a classical force field. In this work we employed the Merck molecular force field MMFF94 [START_REF] Halgren | Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94[END_REF], which uses parameters derived from ab initio computational data, mainly calculated at HF/6-31G* level of theory, except torsional parameters which are taken from MP4SDQ/TZP calculations on selected models. Semiempirical methods are simplified versions of Hartree-Fock theory using empirical corrections in order to improve performance. They are mainly based on the Neglect of Differential Diatomic Overlap (NDDO) integral approximation. We have used the modified neglect of differential overlap MNDO [START_REF] Dewar | Ground states of molecules. 38. The MNDO method. Approximations and parameters[END_REF], the Austin model 1 AM1 [START_REF] Dewar | Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model[END_REF] and the parametric model number 3 PM3 [START_REF] Stewart | Optimization of parameters for semiempirical methods I. Method[END_REF][START_REF] Stewart | Optimization of parameters for semiempirical methods II. Applications[END_REF][START_REF] Stewart | Optimization of parameters for semiempirical methods. III Extension of PM3 to Be[END_REF] methods.

Ab initio methods are based on the computational resolution of the electronic Schrodinger equation. The first approximation uses the Hartree-Fock HF method [START_REF] Slater | A Simplification of the Hartree-Fock Method[END_REF], which rejects the electron correlation energy. Post-Hartree-Fock methods, as those based on the Møller-Plesset perturbation theory, start from the HF results and introduce corrections for the electron correlation through the different perturbation orders. In this work, we have employed the second-order correction in the frozen core MP2 approximation [START_REF] Chr | Note on an Approximation Treatment for Many-Electron Systems[END_REF].

In contrast with ab initio methods, density functional theory (DFT) methods are based on the Hohenberg-Kohn paradigm [START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF][START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF]. From the wide range of functionals, B3LYP is one of the most popular arising from the combination of Becke's exchange functional [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF] together with Lee, Yang and Parr correlation functional [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF]. However, this functional has a poor description of dispersion forces and it is necessary to include them through different empirical corrections as that used in this work, the GD3 correction proposed by Grimme (B3LYP-D3) [START_REF] Grimme | A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[END_REF].

In this work we are mainly employed Pople´s split-valence basis sets [START_REF] Ditchfield | Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules[END_REF] 6-31G, 6-31+G(d,p) and 6-311++G(2d,p). Some of these bases incorporate diffuse functions to describe the heavy atoms (+) and the hydrogen atoms (++) and d or 2d polarization functions for the heavy atoms and p-type functions for the hydrogen atoms. These further improve the description of non-covalent interactions in order to obtain better accuracy and reliability of the predictions.

Results and discussion

Conformational analysis

As for other amino acids [START_REF] Suenram | Millimeter wave spectrum of glycine. A new conformer[END_REF][START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF][START_REF] Blanco | Revealing the multiple structures of serine[END_REF][START_REF] Lesarri | The Shape of Neutral Valine[END_REF][START_REF] Cocinero | The Shape of Leucine in the Gas Phase[END_REF][START_REF] Lesarri | Coded Amino Acids in Gas Phase: The Shape of Isoleucine[END_REF][START_REF] Alonso | Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study[END_REF], Agl presents a complex conformational panorama due to the combinations of intramolecular hydrogen bonds between the acid and the amino groups. In a general way, for amino acids, these interactions, schematized in Figure 1, have been labeled I, II and III. When the acid group presents a cis-COOH disposition it acts as a proton acceptor, as in I and III configurations, while for the trans-COOH arrangement it acts as a proton donor, as in type II configuration. The interaction that stabilizes type I conformers is a single or bifurcated N-H•••O=C hydrogen bond. In type II the main interaction is an O-H•••N hydrogen bond between the hydroxy moiety of the carboxylic group and the nitrogen of the amino group. In the III family, the main interaction is an N-H•••O-H hydrogen bond. These interactions give rise to the three basic structures found for Gly, although conformer III has not been observed experimentally due to conformational relaxation to form I in the supersonic jet [START_REF] Godfrey | Shape of Glycine[END_REF]. However, the presence of a second amino group in the Cα of Agl increases considerably the interaction possibilities because both amino groups can interact simultaneously with the acid group and between them. As a consequence, we have named the conformers of Agl following the same labeling scheme as used in natural amino acids by assigning the main interaction in each case, to that with the smallest hydrogen bond length (see Figure 2). The conformational search on Agl was done using different computational methods as it is shown in Table 1. After the search, a geometry optimization was done for each one of them at MP2 and B3LYP-D3 methods with 6-311++G(2d,p) basis set in order to improve the results and have a realistic prediction of the final number of conformers, because some configurations obtained with low-level calculations converge to other forms already predicted. Harmonic frequency calculations were also done at the same levels of theory to corroborate that all the predicted conformers are true minima. This allows us to discover the reliability of each method initially employed in the conformer search. The number of conformers found in the first step and those found after optimization are given in Table 1.

Table 1. The number of stable species found for each different low-level computational method employed in the conformational search, and the number of stable conformers determined from them after their geometry optimization. As we can see in Table 1, HF/6-31+G(d,p), the highest level computational method is predicting the highest number of conformations, and therefore the optimum method to analyze the conformational landscape of Agl. We compared the conformers obtained between the different methods to corroborate that all of them predict the same structures. Surprisingly, apart from the 17 conformers obtained with the HF/6-31+G(d,p) method, there is an extra conformer (Ic, see Figure 2) that is only predicted by the low-level methods, molecular mechanics MMFF94 force field, and the PM3 or MNDO semiempirical methods. The 15 conformers with energies relative to the global minimum (IIa) lower than 2000 cm - 1 /25 kJ•mol -1 are shown in Figure 2. At this point, observing the different conformers we noticed that some of them only differ in the position of the hydrogen atoms of one of the amino groups, for example, IIa, IIc, and IId.

Computational Method Conformational

We have analyzed the interconversion between these species through the N-Cα torsion. We have calculated from a relaxed scan the potential energy as a function of the dihedral angle φ (H-N-Cα-C') which allows the rotation of the amino group over the N-Cα bond. This energy profile predicts the interconversion pathway between IIa, IIc and IId species (see Figure 3). The small interconversion barriers of tens of wavenumbers from IId to IIc and IIc to IIa would allow their subsequent conformational relaxation to the most stable IIa form in a supersonic expansion [START_REF] Ruoff | Relaxation of conformers and isomers in seeded supersonic jets of inert gases[END_REF]. On the other hand, type I and type III conformers can be interconverted by the exchange of the OH and the C=O groups through the internal rotation of the COOH group, while the rest of the structure remains almost unaltered, as happens for Ia and IIIa conformers. Thus, as well as the other I and III conformers, they can be interconverted through the torsion of the Cα-C' bond, which allows the rotation of the carboxylic group. The Ia-IIIa interconversion potential energy profile was calculated from a relaxed scan varying the dihedral angle τ (N-Cα-C'=O) (see Figure 4). This predicts an interconversion energy barrier of more than 1200 cm -1 , which hinders the rotation of the acid group, and consequently the torsion over the Cα-C' bond, avoiding the interconversion between the III and the I families. Generally, the stabilization of the III type conformers is caused by the existence of some interaction blocking the movement of the acid group. In the amino acids with aliphatic chains, this interaction does not exist or is extremely weak, such as it happens in glycine [START_REF] Godfrey | Shape of Glycine[END_REF], alanine [START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF], valine [START_REF] Lesarri | The Shape of Neutral Valine[END_REF], leucine [START_REF] Cocinero | The Shape of Leucine in the Gas Phase[END_REF] and isoleucine [START_REF] Lesarri | Coded Amino Acids in Gas Phase: The Shape of Isoleucine[END_REF]. However, in amino acids with polar functional groups, such as serine [START_REF] Blanco | Revealing the multiple structures of serine[END_REF] or threonine [START_REF] Alonso | Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study[END_REF], there are intramolecular interactions that further stabilize and fix the arrangement of the acid group. In the case of IIIa conformer of Agl, it is stabilized by the interaction between the two amino groups and the acid group.

Prediction of the rotational spectra

Previous studies of the molecular structure of amino acids [START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF][START_REF] Blanco | Revealing the multiple structures of serine[END_REF][START_REF] Blanco | Conformations of γ-Aminobutyric Acid (GABA): The Role of the n→π* Interaction[END_REF][START_REF] López | Decoding the Structure of Non-Proteinogenic Amino Acids: The Rotational Spectrum of Jet-Cooled Laser-Ablated Thioproline[END_REF], reported that MP2 and B3LYP-D3/6-311++G(2d,p) computational calculations predict equilibrium structures that are in good agreement with the experimentally determined molecular structures. Due to the absence of experimental information regarding the molecular structure of Agl, we have considered these calculations as a reliable prediction of the equilibrium structure of Agl. In addition, the quadrupole coupling constants due to the presence of 14 N atoms also give information on the orientation of the amino groups, which will be helpful for distinguishing conformers with similar rotational constants and are necessary for the accurate prediction of the rotational spectra. Consequently, the complete set of parameters, including rotational constants, quadrupole coupling constants, and electric dipole moment components, for the lower energy conformers of Agl, necessaries for the prediction of their rotational spectra, are listed in Table 2. 2, while 14 N2 is the one of the amino group facing downwards). a , b and c are the electric dipole moment components along the principal inertial axes. E are the calculated electronic energies relative to the global minimum IIa conformer. Gibbs are the calculated Gibbs energies relative to the global minimum IIa conformer.

As it was concluded in previous studies of laser-ablated amino acids such as alanine [START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF], it can be expected that the population of the different conformers of Agl in the supersonic jet is close to that of thermodynamic equilibrium at the temperature of the carrier gas, given that a high collisional rate exists at the beginning of the expansion. In addition, we assume that the collisional relaxation processes occurring in the supersonic jet would alter the equilibrium population of the molecular systems in vibrational states of IId and IIc forms bringing them to the lowest vibrational state of conformer IIa. As a result, it is possible to relate the equilibrium distribution of the conformers with the relative population ratio of them in the expansion. Thus, we have predicted the equilibrium relative populations of the conformers of Agl at 298K from the calculated Gibbs energies. The predicted relative populations for the most stable forms are N IIa/N Ia/ N Ib/ N Ic/ N IIIa/ N IIIb/ N IIb = 100:34:16:9:8:7:6. This population can be related to the relative intensities of the free jet rotational spectra. The intensities of the µa/b/c-type transitions of the i conformer, with population Ni, are proportional to (µa/b/c)i 2 •Ni in a chirped-pulse Fourier transform microwave spectrometer [START_REF] Brown | A broadband Fourier transform microwave spectrometer based on chirped pulse excitation[END_REF], where (µa/b/c)i are the corresponding components of the electric dipole moment along the a, b or c principal inertial axis [START_REF] Gordy | Microwave molecular spectra[END_REF] (see Table 2). Therefore, the obtained relative intensity ratios are IIa/Ia/Ib/Ic/IIIa/IIIb/IIb = 100:0:0:1:0:0:4 for the µa-type transitions, IIa/Ia/Ib/Ic/IIIa/IIIb/IIb = 100:51:16:0:0:5:3 for the µb-type and IIa/Ia/Ib/Ic/IIIa/IIIb/IIb = 100:4:14:2:22:3:0 for the µc-type transitions. According to this, the conformers IIa and Ia will have the most intense spectra but given the sensitivity of the CP-FTMW spectrometers other forms could be expected to be observed. The rigid rotor rotational spectra [START_REF] Gordy | Microwave molecular spectra[END_REF] of the IIa and Ia conformers scaled for the relative intensities have been predicted and are shown in Figure 5 for the 2-8 GHz frequency range. Comparing the structures and the conformational stability for Agl with other amino acids it is interesting to remark that considering the two most stable structures in this case the type II structure prevails over the type I one in stability. This is in contrast with the aliphatic amino acids glycine [START_REF] Suenram | Millimeter wave spectrum of glycine. A new conformer[END_REF], alanine [START_REF] Blanco | The Gas-Phase Structure of Alanine[END_REF], valine [START_REF] Lesarri | The Shape of Neutral Valine[END_REF], leucine [START_REF] Cocinero | The Shape of Leucine in the Gas Phase[END_REF] and isoleucine [START_REF] Lesarri | Coded Amino Acids in Gas Phase: The Shape of Isoleucine[END_REF], for which the most stable conformer, type I, is stabilized by a bifurcated N-H•••O=C intramolecular hydrogen bond with a cis-COOH arrangement. Moreover, in all of these cases type II conformers were observed to be of higher energy, with a N•••H-O intramolecular interaction and consequently a trans-COOH arrangement of the acid group. This is also the case of one structural derivative of glycine, the noncoded aliphatic α-aminobutyric acid [START_REF] Cocinero | Conformations of α-Aminobutyric Acid in the Gas Phase[END_REF]. Interestingly, although the N•••H-O interaction is predicted to have a larger stabilization effect (favouring the type II conformers) [START_REF] Császár | Conformers of Gaseous α-Alanine[END_REF] the prevalence of the lowest energy type-I forms has been attributed to a cooperative stabilizing effect caused by the cis-arrangement of the acid group [START_REF] Császár | In pursuit of the ab initio limit for conformational energy prototypes[END_REF]. This cis-COOH stabilization effect could also be the cause of the dominant I forms in the cases of serine [START_REF] Blanco | Revealing the multiple structures of serine[END_REF] and threonine [START_REF] Alonso | Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study[END_REF], where they have only one N-H•••O=C intramolecular hydrogen bond but are still more stable than the II type conformers, even in the case that they are further stabilized by an intramolecular sequential cycle. This was also observed for phenylglycine [START_REF] Sanz | The Conformers of Phenylglycine[END_REF], one of the structural derivatives of glycine amino acid. However, in the case of our glycine´s derivative, Agl, we consider that the hydrogen bond networks s causes a higher stabilization in form IIa that in conformer Ia. This enhanced stabilization occurs even if the former has a trans-COOH arrangement of the carboxylic group also because it presents a sequential cycle of O-H

•••N, N-H•••N and N-H•••O=C intermolecular interactions. The tipe II N•••H-O interaction
also prevails in the observed conformers of phenylalanine molecule [START_REF] Pérez | Jet-Cooled Rotational Spectrum of Laser-Ablated Phenylalanine[END_REF] but in this case this structure is further stabilized for a N-H•••π intramolecular interaction between the amino and the ring groups.

Conclusions

We have investigated theoretically the conformational landscape of α-aminoglycine and the equilibrium structures of their most stable conformers. From the comparison of the results reached with the different low-cost methods employed in the conformational search, we have concluded that HF/6-31+G(d,p) is the best method in the first steps of the conformational search and analysis, but it should also be complemented with other methods such as molecular mechanics or semiempirical methods to reach a complete conformational landscape. We obtain 15 conformers in an energy interval of 2000 cm -1 from the global minimum. Further investigation of the potential energy surface to investigate possible interconversion coordinates concludes that some of the predicted conformers are associated with potential energy profiles suggesting that some of them presumably do not hold vibrational states and have barriers that allow their relaxation in a supersonic jet to a more stable conformer. Taking into account this, it is possible to conclude that Agl molecule presents a maximum number of 12 stable energy conformers. Their equilibrium structures have been predicted at MP2/6-311++G(2d,p) and B3LYP-D3/6-311++G(2d,p) levels of theory. These can be taken as good approximations of the molecular structure of Agl given the lack of experimental results in this case. The relative populations in the supersonic jet for a potential experiment in rotational spectroscopy, have been calculated, and, considering the possible conformational relaxations, we conclude that only the most populated conformers, would have observable spectra. The rotational spectra of the IIa and Ia species have been predicted taking into account their relative intensity estimations. The main intramolecular interaction of the global minimum IIa form is an O-H•••N-H type II interaction, but it also presents an N-H•••O=C type I hydrogen bond and an N-H•••N-H weaker interaction closes a sequential cycle which further stabilizes this species due to cooperativity. We think that this is the main reason that in this molecule type II conformers prevail in stability against type I ones, in opposition to the observed in most of the other amino acids studied experimentally until now.

Funding:

CR, AM, JCL and SB acknowledge the Junta de Castilla y Leon (Grant INFRARED-FEDER IR2020-1-UVa02) and the Ministerio de Economía y Competitividad (Grant CTQ2016-75253-P).

Fig. 1 .

 1 Fig. 1. Labeling of the main hydrogen bond intramolecular interaction in amino acids (Gly R=H, Agl R= NH2).

Fig. 2 .

 2 Fig.2. The most stable conformers predicted for AgI, labeled following the type I, II and III criteria (see text) and their relative energies (cm -1 ) predicted at the MP2/6-311++G(2d,p) / B3LYP-D3/6-311++G(2d,p) levels of theory. The conformers marked with an * might relax species IIa in a supersonic expansion (see text).

Fig. 3 .

 3 Fig. 3. Potential energy function for the rotation around the N-Cα bond (φ = H-N-Cα-C') connecting the IId, IIc and IIa conformers calculated at B3LYP-D3/6-311++G(2d,p) level of theory.

Fig. 4 .

 4 Fig. 4. Potential energy function for the rotation around the Cα-C' bond (τ =N-Cα-C'=O) connecting the IIIa and Ia conformers calculated at B3LYP-D3/6-311++G(2d,p) level of theory.

Fig. 5 .

 5 Fig. 5. Predicted rotational spectra of the IIa and Ia conformers of Agl in the 2-8 GHz frequency range.

Fig. 6 .

 6 Fig. 6. Predicted molecular structures of IIa and Ia conformers of Agl. The doted lines shown the possible hydrogen bonds formed and their calculated distances (in Å) at B3LYP-D3/6-311++G(2d,p) level of theory.

Search Geometry Optimization

	MMFF94	23	11
	AM1	20	11
	PM3	22	13
	MNDO	22	12
	HF/6-31G	24	14
	HF/6-31+G(d,p)	27	17

Table 2 .

 2 Rotational parameters and relative energies for the conformers of Agl predicted at B3LYP-D3/6-311++G(2d,p) level of theory.

	Param. a	IIa	Ia	IIb	Ib	IIc	IIIa	IIIb
	A/MHz	5013.2	5215.2	5149.1	5242.2	4999.2	5158.0	5188.2
	B/MHz	3537.9	2939.9	3162.0	3266.8	3467.0	2845.1	3371.5
	C/MHz	2189.4	2448.5	2384.2	2206.1	2166.9	2576.5	2150.8
	14 Na 3/2(aa)/MHz	2.807	-1.712	1.917	3.089	-6.421	-6.752	3.346
	14 Na 1/4(bb-cc)/MHz	1.179	-0.693	0.568	1.592	0.109	-	1.879
	14 Nb 3/2(aa)/MHz	-6.575	2.544	-6.920	-5.576	-1.627	1.699	-6.167
	14 Nb 1/4(bb-cc)/MHz	0.015	1.507	-0.013	0.126	-0.645	1.064	0.353
	µa/D	4.6	-0.5	-3.8	-0.7	-3.3	-0.6	0.7
	µb/D	1.4	1.7	1.0	1.4	1.8	-0.3	1.2
	µc/D	1.4	0.5	-0.4	1.3	-0.1	2.3	0.9
	ΔE/cm -1	0.0	487.2	522.4	561.6	597.3	734.8	752.0
	ΔGibbs/cm -1	0.0	188.7	549.1	350.1	378.8	488.8	514.4
	Param.	Ic	Id	IId	IIId	Ie	IIe	IIIe
	A/MHz	5209.7	5203.5	4980.5	5145.2	5154.3	5151.7	5132.4
	B/MHz	2735.2	3211.6	3519.5	3285.4	3401.5	3093.5	2723.5
	C/MHz	2644.4	2295.5	2189.1	2269.4	2153.1	2423.8	2659.5
	14 N1 3/2(aa)/MHz	0.609	2.872	-1.911	3.279	-0.289	2.297	-6.754
	14 N1 1/4(bb-cc)/MHz	-0.706	0.349	-0.702	1.346	-0.855	0.583	2.443
	14 N2 3/2(aa)/MHz	0.618	3.232	3.792	1.658	1.757	-0.725	-6.755
	14 N2 1/4(bb-cc)/MHz	-0.691	1.330	0.552	-3.990	3.098	-1.220	0.244
	µa/D	1.7	-0.9	4.7	1.6	-1.2	-5.7	1.1
	µb/D	0.0	2.6	2.7	0.2	-0.4	1.8	0.0
	µc/D	-0.6	0.9	-0.6	0.0	1.1	-0.6	1.8
	ΔE/cm -1	768.8	1239.8	1339.2	1414.2	1462.8	1656.1	1825.1
	ΔGibbs/cm -1	460.5	1082.4	1040.7	1065.8	965.0	1533.5	1184.1

a A, B and C are rotational constants. aa, bb and cc are 14 N nuclear quadrupole coupling constants ( 14 N1 is the nitrogen of the amino group facing upwards according to Figure

Acknowledgments

13 CR, AM, JCL and SB acknowledge the Junta de Castilla y Leon (Grant INFRARED-FEDER IR2020-1-UVa02) and the Ministerio de Economía y Competitividad (Grant CTQ2016-75253-P).

Declaration of interests

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☒ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alberto Macario, Carlota Rodriguez, Susana Blanco, Juan Carlos Lopez reports financial support was provided by Junta de Castilla y Leon Consejeria de Educacion. Alberto Macario, Carlota Rodriguez, Susana Blanco, Juan Carlos Lopez reports financial support was provided by Ministry of Economic Affairs and Digital Transformation.

Conflict of Interest


William Wheeler
email: william.wheeler@univ-lyon1.fr

Ali Sari

Pascal Venet

Yann Bultel

Elie Riviere

Prognosis of the RUL in 2 nd life applications based on the diagnosis of degradation modes LFP battery aging behavior: diagnosis of cell materials for second life applications

 The battery sorting process is essential in achieving & ensuring reliability of batteries in 2 nd life Batteries from electric vehicles : different ageing due to design, use and environment 2 nd life batteries must be guaranteed for a specified time and use Sudden shift in cell ageing may appear: capacity loss, resistance increase [1-3] Prognosis of the remaining useful life requires a diagnosis of aging modes to understand changes [4]  This poster proposes a method to characterize graphite / lithium iron phosphate (C/LFP) cells Loss of Lithium Inventory (LLI) Loss of Active Material at the negative electrode (LAM NE )

PROPOSED SOH neg ESTIMATION METHODS

8. FUTUR WORK



  neg ESTIMATION RESULTS[1] S.F. Schuster, T. Bach, E. Fleder, J. Müller, M. Brand, G. Sextl, A. Jossen, Nonlinear aging characteristics of lithium-ion cells under different operational conditions, J. Energy Storage. 1 (2015) 44-53. doi:10.1016/j.est.2015.05.003. [2] M. Klett, R. Eriksson, J. Groot, P. Svens, K. Ciosek Högström, R.W. Lindström, H. Berg, T. Gustafson, G. Lindbergh, K. Edström, Non-uniform aging of cycled commercial LiFePO4//graphite cylindrical cells revealed by post-mortem analysis, J. Power Sources. 257 (2014) 126-137. doi:10.1016/j.jpowsour.2014.01.105. [3] M. Safari, C. Delacourt, Aging of a Commercial Graphite/LiFePO4 Cell, J. Electrochem. Soc. 158 (2011) A1123. doi:10.1149/1.3614529. [4] M. Dubarry, C. Truchot, B.Y. Liaw, Synthesize battery degradation modes via a diagnostic and prognostic model, J. Power Sources. 219 (2012) 204-216. [5] L. Zheng, J. Zhu, D.D.C. Lu, G. Wang, T. He, Incremental capacity analysis and differential voltage analysis based state of charge and capacity estimation for lithium-ion batteries, Energy. 150 (2018) 759-769. doi:10.1016/j.energy.2018.03.023. REFERENCES  Cell State of Health (SoH cell )  Fast SoH cell decrease for all the cells in the first hundred cycles  Fast decrease of SoH cell for cells 7,8 & 9 after 700-1000 cycles  The estimation method makes it possible to differentiate:  Aging dynamics between cell and negative electrode  Aging of the negative electrode accelerates during use  Correlation between cell and negative electrode for the aging acceleration  End of the experimental tests : planned for SoH cell = cell 12 ∘, 13 ×, 14 * CC-CV 3.65 V 2C WLTP C/3 70 % 18650 cell 15 ∘, 16 ×, 17 * CC-CV 3.55 V 2C WLTP C/3 70 % 18650 cell 18 ∘, 19 ×, 20 * CC-CV 3.65 V 2C CC 2C 70 % 18650 cell 20 ∘, 21 ×, 23 * CC-SoH neg negative electrode follow-up  Based on full-cell measurement and phase transition detection using ICA/DVA  SoH neg negative electrode estimation  Step 1 : 𝛥𝑄 𝑛𝑒𝑔 = 𝑄 𝐿𝑖𝐶 𝑎 -𝑄 𝐿𝑖𝐶 𝑏 [

-Q 0 :

 0 initial cell capacity -Q max (t) : maximum cell capacity at time t  Electrode material characterisation 18650 fresh cylindrical cells (18650) dismantling in glove box Electrode characterisation in half cell vs. Li/Li + (coin cell CR2032) Open Circuit Potential (OCP) of each electrode (figures  & ) Negative electrode phase transition detection using ICA/DVA [5] (figure ) No characteristic transition for the positive electrode  Cell voltage profile (OCV) reconstruction  Enable negative electrode phase transition detection on full-cell measurement (figure (a)) & allow SoH neg estimation (section 5)  Possible ageing scenarios LLI (Loss of Lithium Inventory) : offset ∆𝐐 𝐋𝐋𝐈 increase between electrode OCP (figures (a) & (b)) LAM NE (Loss of Active Materials at the Negative Electrode) : shrink of negative electrode OCP (figure (b) & (c)). Lower charge/discharge capacity between phase transitions, ΔQ neg decrease LLI + LAM NE : combination of both effects: offset increase and negative electrode shrinking. Estimations methods 1 and 2 are rendered unusable after a certain number of cycles: between 1000 and 3500 depending on the cell  LLI is too great  LiC 12 phase transition disappears in cell voltage profile (figures (a) & (b)) Estimations methods 3 and 4 works on all lifecycle  Lower accuracy due to the use of closer phase transition  SoH neg loss accelerates during use  Fast SoH neg decrease for cells with fast decrease of SoH cell (cells 7, 8 & 9 with 100% DoD, in red) The results of the four SoH neg estimations are presented below. Colors correspond to cells in the table in section 2 "experiments".

  Estimation SoH neg 𝑳𝒊𝑪 𝒂 𝑺𝒐𝑪 𝒏𝒆𝒈 𝒂 𝑳𝒊𝑪 𝒃 𝑺𝒐𝑪 𝒏𝒆𝒈 𝒃

	4. ELECTRODE CHARACTERISATION
	Method 1	𝐶	0	𝐿𝑖𝐶 12	0,6
	Method 2	𝐿𝑖𝐶 54	0,1	𝐿𝑖𝐶 12	0,6
	Method 3	𝐿𝑖𝐶 54	0,1	𝐿𝑖𝐶 18	0,3
	Method 4	𝐿𝑖𝐶 36	0,16	𝐿𝑖𝐶 18	0.3

𝑺𝒐𝑯 𝒄𝒆𝒍𝒍 = 𝟏𝟎𝟎 * 𝑸 𝒎𝒂𝒙(𝒕)

𝑸 𝑶

[%]


Santiago Pantano-Calderón

Claude Baron
email: baron@insa-toulouse.fr

Jean-Charles Chaudemar
email: jean-charles.chaudemar@isae-supaero.fr

Élise Vareilles
email: elise.vareilles@isae-supaero.fr

Rob Vingerhoeds
email: rob.vingerhoeds@isae-supaero.fr

Regarding the COVID

Keywords: COVID-19, Crisis, Modeling, Simulation, Holistic approach

come

INTRODUCTION

In the very beginning of 2022, humanity is still fighting the most important public health crisis of the last years, the pandemic caused by the COVID-19 (OECD 2020a;OECD 2020b). At this point, it is possible to assert that governments have settled on an universal way to reduce the impacts of the coronavirus pandemic, placing trust in vaccination plans, lockdowns and simple health recommendations [START_REF] Mallah | COVID-19: breaking down a global health crisis[END_REF][START_REF] Alfano | The Efficacy of Lockdown Against COVID-19: A Cross-Country Panel Analysis[END_REF][START_REF] Xing | Efficacy and safety of COVID-19 vaccines: a systematic review[END_REF]). An example of this is the insistent call to take booster shots of COVID-19 vaccines in order to contain the wave of infections of January 2022, presumably caused by the Omicron variant [START_REF] Abbany | COVID: Have we reached the peak of omicron infections?[END_REF]. Either by countermeasures taken or the characteristics of this variant, a far fewer number of deaths than previous waves has been observed in most of countries [START_REF] Abbany | COVID: Have we reached the peak of omicron infections?[END_REF][START_REF] Joly | COVID in Europe: France reports 'tidal wave' of new infections as records broken in Italy[END_REF]). However, around 5.5 millions of deaths were reported in the first two years of the pandemic (WHO 2022) and the virus is still threatening the stability of healthcare sector [START_REF] Joly | COVID in Europe: France reports 'tidal wave' of new infections as records broken in Italy[END_REF].

The COVID-19 outbreak forced humanity to act rapidly, even if there was not enough knowledge to make wellinformed decisions (Brinks and Ibert 2020) and, indeed, in this state of emergency, there was a necessity to act as no acting would have leaded to a worse situation [START_REF] Nazir | Study of COVID-19 mathematical model of fractional order via modified Euler method[END_REF]. This characteristics of urgency, uncertainty and threat lead the entire globe into a deep crisis that affected not only the healthcare system but also economic, WiPe Paper -Analytical Modeling and Simulation Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 Hedi Karray, Antonio De Nicola, Nada Matta, Hemant Purohit social and political sectors [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF][START_REF] De Weck | Handling the COVID-19 crisis: Toward an agile model-based systems approach[END_REF]. This means that societies, and especially power agents such as governments, are not trying to control a pure health crisis, but a systemic crisis that requires an holistic approach to respond to [START_REF] De Weck | Handling the COVID-19 crisis: Toward an agile model-based systems approach[END_REF].

Therefore, as the pandemic is still threatening society and the crisis withstand all countermeasures applied until present, it is completely necessary to find tools that allow scientists to propose the best alternatives facing public health crises. Modeling and simulation has been proven to satisfactorily replicate and predict the behavior of complex systems [START_REF] Abhishek | Weather Forecasting Model using Artificial Neural Network[END_REF][START_REF] Batstone | The IWA Anaerobic Digestion Model No 1 (ADM1)[END_REF], and during these last years, as a result of the COVID-19 outbreak, different models have been proposed to reproduce the behavior of specific aspects of the pandemic in order to understand the occurring phenomenon [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF][START_REF] Arino | A simple model for COVID-19[END_REF][START_REF] De Weck | Handling the COVID-19 crisis: Toward an agile model-based systems approach[END_REF]. However, most of proposed models focus on its epidemiological characteristics and omit the real range of the crisis, where social and economic factors are closely involved.

For this reason, this paper has the purpose to contend the necessity of using systemic and holistic model-based approaches, not only to confront the current crisis but also to aid informed decision-making for future public health events. After this introduction the current modeling for the COVID-19 crisis is presented. In the next section, some advantages of using systems engineering methods are identified to generate a more realistic model of the pandemic, and the possibility to call systems analysis and control theory concepts is contended to better visualize the crisis.

The last section proposes a discussion and recommendations for future works.

THE MODELS FOR THE CRISIS

Modeling and simulation are tools currently in use when studying the COVID-19, as they may be able to replicate the behavior of different variables involved in its corresponding epidemiology, such as the dynamics of the transmission of the virus or its mortality. This reproduction helps scientists and governments to predict the progress of the virus in the population over time, and so, it supports the decision-making facing the emergency. In this order of ideas, models are potentially useful to anticipate infection waves and new focal points, and they can help authorities to create strategies to limit the propagation of the disease, for example, imposing lockdowns or individual quarantines, limiting the transit in borders and airports or redistributing the available vaccine doses.

Current models of the pandemic are based on both medical and non-medical parameters [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF]. For example, the medical parameters are several statistical and epidemiological indicators such as the transmissibility of the virus, the incubation period, proportion of asymptomatic infections and virus lifespan [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF][START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF][START_REF] Arino | A simple model for COVID-19[END_REF]. On the other hand, among the non-medical parameters, it is possible to find geographical statistics and demographic data, such as population, birth and death rates, age and gender [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF][START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF]. Even if there are several parameters that can be easily identified when building a pandemic model, there are many other hidden factors that may strongly affect the transmission or mortality of the virus, and this is the main reason why the behavior of the COVID-19 should be observed from a holistic approach.

The complexity of the pandemic

There are numerous reasons why the evolution of a pandemic is difficult to model and foresee. First, the measures taken by the governments and the appearance of novel variants of the virus cause variations in the infections rate, therefore, the transmissibility of the disease is not constant over time [START_REF] Alfano | The Efficacy of Lockdown Against COVID-19: A Cross-Country Panel Analysis[END_REF][START_REF] Xing | Efficacy and safety of COVID-19 vaccines: a systematic review[END_REF][START_REF] Chowdhury | Long-term strategies to control COVID-19 in low and middle-income countries: an options overview of communitybased, non-pharmacological interventions[END_REF]). On the other hand, economic, social, cultural and political factors may be involved in the strategies proposed by authorities confronting the crisis. For instance, even if the imposition of general quarantines proved to be an effective way to reduce the transmission of the virus among people (Alfano and Ercolano 2020), the implementation of long lockdowns is an inviable alternative due to large costs not related to epidemiological factors, as it causes huge economic loses and several social and psychological problems in medium and long term [START_REF] Michalski | The Economic Impact of Different COVID-19 Lockdown Strategies in France[END_REF][START_REF] Brooks | The psychological impact of quarantine and how to reduce it: rapid review of the evidence[END_REF].

Furthermore, some cultural, demographic and social aspects may play an important role in the transmission of the virus [START_REF] Bayeh | The Social Lives of Infectious Diseases: Why Culture Matters to COVID-19[END_REF]. Cultural practices and habits, such as the population beliefs, the gender roles and the discipline and obedience of people, may influence the infectious rate. In the present pandemic, more men than women have been hospitalized or have died by COVID-19 related causes [START_REF] Cañelles López | Coronavirus: 3 datos que explican por qué la covid-19 afecta de manera diferente a hombres y mujeres[END_REF][START_REF] Jin | Gender Differences in Patients With COVID-19: Focus on Severity and Mortality[END_REF], and some authors propose that the difference of severity and mortality rates between men and women may correspond to gendered behavioral aspects and gender-segregated occupations and not to pure biological factors [START_REF] Galasso | Gender differences in COVID-19 attitudes and behavior: Panel evidence from eight countries[END_REF][START_REF] Shattuck-Heidorn | What's Really Behind the Gender Gap in Covid-19 Deaths?[END_REF]). In the same way, populations with psychological predispositions to reject scientific researches suffer bigger risks of aggravation of the emergency [START_REF] Bayeh | The Social Lives of Infectious Diseases: Why Culture Matters to COVID-19[END_REF].

Mathematical and data science techniques are largely employed to predict the progress of the pandemic and, certainly, the sources and amounts of data collected have an important role in forecasting [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF]). On the basis of analytical approaches, different mathematical models have been proposed to replicate the evolution of the number of infections over time, for example, the Bats-Hosts-Reservoir-People (BHRP) model, simplified to Reservoir-People (RP) model, which is expressed in six differential equations [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF], and the computational model on COVID-19 based on cellular automata [START_REF] Ghosh | Computational Model on COVID-19 Pandemic Using Probabilistic Cellular Automata[END_REF]. However, the main issue that we found is that most of traditional approaches used today do not fit the reality as expected since they usually concentrate only on the epidemiological aspects of the disease.

The suitability of a traditional model

In order to analyze the reliability and suitability of traditional analytical models, we tested the BHRP transmission network model, proposed by [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF], since it is one of the nine most commonly used models based on mathematical implementations (AlArjani et al. 2022) and it is an extension of another traditional compartmental model in epidemiology, the Susceptible-Infectious-Recovered (SIR) model [START_REF] Chen | Investigation of Key Interventions for Shigellosis Outbreak Control in China[END_REF]. The major contribution of this approach stands in the consideration of the complete transmission route from the bats to the people through the seafood market in Wuhan, China [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF]), though the model was simplified into a RP model and normalized in order to explore it more clearly. Afterwards, the normalized RP model can be used to calculate the basic reproduction number 𝑅 0 to evaluate the transmissibility of the SARS-COV2 [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF]). This model is also capable to estimate and reproduce the dynamic of transmission of the virus by introducing several epidemiological parameters: Incubation period, duration of symptoms, fraction of asymptomatic infections and lifespan of the virus in the reservoir. A population and its birth and death rates are also required to perform a simulation.

In order to test the model, we collected the data of the epidemic curve of Bogota, Colombia, from February 26 th , 2020, date of the first reported case in the city, to June 5 th , 2020 (SALUDATA 2021). The sample frequency of the data is 1 day. The epidemic curve and the date of the implementation of the first lockdown, on March 25 th , 2020, are shown in figure 1. Following the method and the parameter values suggested in [START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF], two curve fitting processes using the method of least squares were performed to estimate the value of the normalized diffusion rate of the virus. A simulation for each curve fitting result was carried out with a step time of 1 day. To do so, and in order to soften the abrupt changes in the epidemic curve, real data was processed by calculating, for each sample, the average of the number of new symptomatic cases of three days, as shown in equation 1, where 𝐼 is the number of new symptomatic cases in the day 𝑖 after the detection of the first symptomatic case. At first, processed real data from February 26 th , 2020 to April 16 th , 2020 were used to do the curve fitting. In a second case, processed real data from April 17 th , 2020 to June 5 th , 2020 were used to perform the same procedure. The corresponding simulation results are shown in figures 2 and 3. The first round of simulation, where the normalized diffusion rate of the virus was estimated using the processed real data of the first 50 days of epidemic, resulted in a simulated behavior completely distant from reality. According to the simulation, we found that, on June 5 th , health authorities should have detected 5,156 new symptomatic cases, but in fact, there were 542 new symptomatic cases reported in Bogota on that day. This discrepancy may be explained by the omission of the lockdown imposed in the city 28 days after the detection of the first infected person, as this probably caused an overestimation of the transmissibility of the disease in the model. This was the reason why a second estimation of the normalized diffusion rate was needed, using the epidemic curve a few weeks after the lockdown was declared, in order to perform a second simulation.

𝐼 𝑖 𝑝𝑟 𝑜𝑐𝑒𝑠𝑠𝑒𝑑 =          𝐼 𝑖 𝑟 𝑒𝑎𝑙 , 𝑖 = 0 ( 𝐼 𝑖-1 𝑟 𝑒𝑎𝑙 + 𝐼 𝑖 𝑟 𝑒𝑎𝑙 )/2, 𝑖 = 1 ( 𝑖 𝑘=𝑖-2 𝐼 𝑘 𝑟 𝑒𝑎𝑙 )/3, 𝑖 > 1 𝑖 ∈ {N ∪ 0} (1)
In the second round, the normalized diffusion rate of the virus was estimated using the processed real data from the day 51 to the day 100 after the first reported case on February 26 th , 2020. This time simulation fit better the real new symptomatic cases over all the 100 days of data collected. Therefore, it was possible to notice that the model would be able to predict the evolution of the epidemic curve, at least, in short term. This was confirmed when the simulation was extended 15 days more, where the simulated data estimate 1,493 new symptomatic cases on June 20 th , 2020, and real data shows 1,397 new symptomatic cases in the city on the same date (SALUDATA 2021), i.e. on that day we found a discrepancy of 96 cases, or 6.9%. Nevertheless, when extending the simulation 15 days more, or 30 days in total until July 5 th , 2020, we clashed with a divergence of 1219 cases, or 65,6%, as simulation estimates 3,076 new symptomatic cases, whereas there were in fact 1,857 new symptomatic cases on that day in Bogota (SALUDATA 2021). previous subsection, the transmissibility of the disease is variable over time due to the health strategies introduced by governments. On the other hand, the virus itself does not remain invariant in time. So far, 12 variants of the SARS-COV2 have been detected and classified (CDC 2021b), each one having its own infection ability and mortality (CDC 2021b). Likewise, the complexity of real relationships was completely omitted in the BHRP model. Overall, this kind of traditional mathematical models, rather usual in the study of the COVID-19 pandemic [START_REF] Shinde | Forecasting Models for Coronavirus Disease (COVID-19): A Survey of the State-of-the-Art[END_REF][START_REF] Chen | A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[END_REF][START_REF] Arino | A simple model for COVID-19[END_REF], are very limited and do not fulfill the fidelity expectations to support the decision-making facing the current crisis.

SYSTEMIC APPROACH OF THE PANDEMIC

After the explanation of the current crisis and the formulation of the problem, it is possible to identify three main characteristics of COVID-19 emergency. To begin with, it exhibit a global impact [START_REF] De Weck | Handling the COVID-19 crisis: Toward an agile model-based systems approach[END_REF], where society find itself out of normal functioning in all essential levels, i.e. in social, economic and heath systems (de Weck et al. 2020; Brinks and Ibert 2020). In addition, there is a strong intrinsic feedback delay when fighting the spreading of the disease, as the virus cannot be detected during its incubation period [START_REF] Winkelhake | If you're fully vaccinated, wait a few days after a COVID-19 exposure before getting tested[END_REF], and the strategies deployed by authorities are often centered in mitigating health issues in short term due to the necessity to respond urgently, omitting medium-term and long-term consequences [START_REF] Simon | Impacts of the Covid-19 lockdown and relevant vulnerabilities on capability well-being, mental health and social support: an Austrian survey study[END_REF][START_REF] Brooks | The psychological impact of quarantine and how to reduce it: rapid review of the evidence[END_REF][START_REF] Michalski | The Economic Impact of Different COVID-19 Lockdown Strategies in France[END_REF]. Moreover, there is also a strong uncertainty bound to the nature of the crisis, as the portion of infections that were not detected by the healthcare authorities is considerably large, around 75% (95% CI1, 70.6% -78.7%) in the U.S. until November 2021 (CDC 2021a). Likewise, uncertainty is bound to the complexity of the human behavior and social relationships [START_REF] Bayeh | The Social Lives of Infectious Diseases: Why Culture Matters to COVID-19[END_REF].

Consequently, in order to move towards an approach capable of replicating the first of the three characteristics of the crisis mentioned previously, i.e., its global impact, it is necessary to construct a holistic framework that takes into account all the involved forming components of society. In this sense, de Weck et al. 2020 managed to identify that there are five primary systems are involved in the COVID-19 pandemic: Biological system, social system, healthcare system, political system and economic system. Indeed, interactions between them must be equally considered. As it was stated in the previous section, models are hardly realistic whether they only consider the biological characteristics of the disease, that is to say, its epidemiology. Additionally, government decisions and economy play an important role in the evolution of the epidemic [START_REF] Alfano | The Efficacy of Lockdown Against COVID-19: A Cross-Country Panel Analysis[END_REF][START_REF] Chowdhury | Long-term strategies to control COVID-19 in low and middle-income countries: an options overview of communitybased, non-pharmacological interventions[END_REF]. Taking into account the previous conceptions, a global framework is proposed in figure 4. This holistic approach derives into a system-of-systems that allows the model to be more loyal and closer to reality. The presented framework implies that the crisis encompasses five different sub-systems, complex interactions, internal feedback loops and a distributed behavior. This ensemble of properties, in turn, indicates that the COVID-19 pandemic should be treated as a complex system. On the other hand, analytical approaches require a prior complete understanding of the system since, to apply them, a detailed description of the behavior of each involved element is needed [START_REF] Aziza | Simulating Complex Systems -Complex System Theories, Their Behavioural Characteristics and Their Simulation[END_REF]). Then, it is possible to realize that pure analytical modeling would not be an advantageous Otherwise, it is also necessary to contend with the existing feedback loop delays and the uncertainties inherent to the crisis. Alone, in its fundamental behavior, the pandemic acts like an unstable open-loop system that grows exponentially [START_REF] Karray | How control theory can help us control COVID-19[END_REF]). However, when infections are detected and health strategies are implemented, the pandemic can be seen as a traditional control system of which feedback signal and control signal are the number of new infections and the countermeasures, respectively. Moreover, control engineering methods are already in use in the containment of the pandemic, for example, when authorities declare a lockdown after the basic reproduction number 𝑅 0 reaches a threshold (BBC Mundo 2020), resembling an on-off control system. Fortunately, as many other systems, pandemics can be stabilized and controlled [START_REF] Karray | How control theory can help us control COVID-19[END_REF]).

On the other hand, regarding the mitigation plans for the COVID-19 pandemic, control theory may provide interesting approaches to respond to the crisis. According to the proposed holistic approach, there are two main feedback signals that authorities use to conceive and introduce health and economic strategies: public health and economic indicators. These feedback signals may have a delay caused by the nature of the crisis, as established in the beginning of this section. Compensating delayed feedback requires prediction, and in order to contend with it, predictive control methods, such as the Smith predictor and the Kalman filter, may be profitable [START_REF] Frank | Time Delays[END_REF].

Likewise, uncertainty can be reduced with predictive control methods, since they can estimate the non-observed variables of the system, and also with adaptive control methods, as they can adapt to different variations on the pandemic parameters over time.

CONCLUSIONS

After contemplating the way the COVID-19 pandemic has been modeled, this paper highlights the need to develop more realistic models to find effective strategies to mitigate the spread of the disease. The imposition of strong health policies led to serious economic impacts in a short time, which caused the deterioration of other forming aspects of society. Consequently, the pandemic requires a systemic approach that considers the different sectors as a whole system in order to understand its multi-level structure, feedback loops and distributed decision-making. This paper is part of a work in progress, and indeed, there are several elements in this analysis that require further elaboration. However, different tools such as systemic approaches, high-complex systems analysis and control theory may be truly useful to understand and model the occurring phenomena, and likewise, systems and control engineering may have an important role to face and mitigate the crisis.

Figure 1 .

 1 Figure 1. Curve of new symptomatic cases per day in Bogota from February 26 th , 2020 to June 5 th , 2020

Figure 3 .

 3 Figure 2. Simulation of the BHRP model using data of the first 50 days of pandemic to perform the estimation of the normalized diffusion rate

Figure 4 .

 4 Figure 4. Holistic approach of the crisis, based on the work of de Weck et al. 2020.

  to model the pandemic. However, systems engineering, and more specifically, systemic approaches may provide the most appropriate modeling methods to reproduce the behavior of the emergency (de Weck et al. 2020), as they are capable to represent a large number of nonlinear interactions, guided by objectives and not by details[START_REF] Aziza | Simulating Complex Systems -Complex System Theories, Their Behavioural Characteristics and Their Simulation[END_REF]).

1Confidence interval WiPe Paper -Analytical Modeling and Simulation Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 Hedi Karray, Antonio De Nicola, Nada Matta, Hemant Purohit method


Morteza Ezzabady

Philippe Muller

Chloé Braud

Multi-lingual Discourse Segmentation and Connective Identification: MELODI at DISRPT2021

We present an approach for discourse segmentation and discourse connective identification, both at the sentence and document level, within the DISRPT 2021 shared task, a multi-lingual and multi-formalism evaluation campaign. 1 Building on the most successful architecture from the 2019 similar shared task, we leverage datasets in the same or similar languages to augment training data and improve on the best systems from the previous campaign on 3 out of 4 subtasks, with a mean improvement on all 16 datasets of 0.85%. Within the Disrpt 21 campaign the system ranks 3rd overall, very close to the 2nd system, but with a significant gap with respect to the best system, which uses a rich set of additional features. The system is nonetheless the best on languages that benefited from crosslingual training on sentence internal segmentation (German and Spanish).

Introduction

Discourse segmentation, the separation of a text or conversation in elementary units that make up the arguments of the rhetorical structure of a text, has long been a neglected step in discourse analysis, considered easy and generally assumed as given in discourse parsing studies, where the focus is to predict the rhetorical structure of a document, a labelled relational structure, with properties dependent on the theorerical framework considered, Rhetorical Structure Theory (RST, [START_REF] Mann | Rhetorical Structure Theory: Toward a functional theory of text organization[END_REF], Segmented Discourse Representation Theory (SDRT, [START_REF] Asher | Logics of Conversation[END_REF], or the Penn Discourse Treebank (PDTB, [START_REF] Prasad | The Penn Discourse Treebank 2.0[END_REF].

However this important step has generated more interest recently, as illustrated by the 2019 shared task at the Discourse Relation Parsing and Treebanking (DISRPT) workshop [START_REF] Zeldes | The DIS-RPT 2019 shared task on elementary discourse unit segmentation and connective detection[END_REF]. This campaign made available several existing corpora in different language in a common format, expressing the task as a sequence tagging problem, where tokens are to be classified as beginning a segment or not, or, in the case of PDTB corpora, being part of a discourse connective signalling a relation between textual arguments. Segmentation in itself has also shown a lot of potential as an auxiliary task in machine translation [START_REF] Chen | Modeling discourse structure for document-level neural machine translation[END_REF] and summarization [START_REF] Xu | Discourse-aware neural extractive text summarization[END_REF], independently of discourse parsing.

DISRPT 2021 shared task reproduces the same setting as DISRPT 2019, with some additional data and minor modifications of the original datasets, segmentation as task 1, connective identification as task 2, and adds the prediction of relations between segments, assuming those are known, as task 3.

The following shows examples from the English datasets, illustrating respectively task 1 and task 2, with intended units to recover marked between brackets:

• [Three seats currently are vacant] [and three others are likely to be filled within a few years] (...)

• [But] [in the end] his resignation as Chancellor of the Exchequer may be a good thing (...)

In the first case, tokens "Three" and "and" would be marked as segment beginnings. In the second case, where the target connectives are "but" and "in the end", beginning tokens "but" and "in" would be marked "B" (begin) and "the", "end", would be marked as "I" (inside). In both examples, other tokens would be marked "out". Since sentences are almost always discourse units in existing frameworks, segmentation can be seen as two sub-problems: detecting sentences, and detecting intra-sentence segment boundaries. To reflect this, the 2019 shared task introduced two sub-tasks for segmentation and connective identification: either sentence-level segmentation, with sentence boundaries given (when annotated, or provided with a sentence splitter otherwise), also informed by syntactic parsing of sentences, or without any of that information.

With the exception of systems presented at DIS-RPT 2019 [START_REF] Bourgonje | Multilingual and cross-genre discourse unit segmentation[END_REF][START_REF] Yu | Gum-Drop at the DISRPT2019 shared task: A model stacking approach to discourse unit segmentation and connective detection[END_REF][START_REF] Muller | ToNy: Contextual embeddings for accurate multilingual discourse segmentation of full documents[END_REF], existing work on segmentation always assumed gold sentences, e.g. [START_REF] Wang | Toward fast and accurate neural discourse segmentation[END_REF][START_REF] Lukasik | Text segmentation by cross segment attention[END_REF].

One interesting aspect of such a task is the availability of comparable data in different languages. This has been leveraged in the past for segmentation (Braud et al., 2017b), but not in the past 2019 campaign, where the best system relied on fine-tuning a contextual language model for each language separately, albeit using the same multilingual embedding model [START_REF] Muller | ToNy: Contextual embeddings for accurate multilingual discourse segmentation of full documents[END_REF].

Here we propose to build on the previous DIS-RPT best system and exploit the availability of multiple corpora for the same language, or the same family of languages (romance, germanic) to augment training of dedicated models.

Combining this approach with a few adjustments to the base model, we manage to improve on many datasets compare to the previous best DISRPT systems, with a mean difference in F1 score of 0.46% and 1.24% on segment boundary detection for sentence and document level respectively, and 3.07% on connective detection for sentences (we didn't improve results at document level for discourse connectives).

Within the Disrpt 21 campaign the system ranks 3rd overall, very close to the 2nd system, but with a significant gap with respect to the best system, which uses a rich set of additional features.

Our code and instructions to reproduce the experiments are available online.2

Related work

Discourse segmentation appeared as an NLP task with the creation of the first annotated RST documents in English, and was primarily rule-based [START_REF] Marcu | The rhetorical parsing of unrestricted texts: a surface-based approach[END_REF]. Since then the literature on discourse parsing generally assumed that elementary discourse units (discourse segments) were given, with only a handful of exceptions [START_REF] Soricut | Sentence level discourse parsing using syntactic and lexical information[END_REF][START_REF] Fisher | The utility of parse-derived features for automatic discourse segmentation[END_REF][START_REF] Tofiloski | A syntactic and lexical-based discourse segmenter[END_REF][START_REF] Hernault | HILDA: A discourse parser using support vector machine classification[END_REF][START_REF] Joty | CODRA: A novel discriminative framework for rhetorical analysis[END_REF], until more recent neural-based work [START_REF] Wang | Toward fast and accurate neural discourse segmentation[END_REF][START_REF] Lukasik | Text segmentation by cross segment attention[END_REF], still at the sentence level, and always on English or Mandarin. Only the work of (Braud et al., 2017b,c) have considered more varied languages, after the creation of a few different datasets in the past ten years (see the Data section below).

The DISRPT 2019 workshop introduced a more general evaluation framework for discourse segmentation with a shared task considering multilingual data, and segmentation both at the sentence and document level [START_REF] Zeldes | The DIS-RPT 2019 shared task on elementary discourse unit segmentation and connective detection[END_REF]. The best system [START_REF] Muller | ToNy: Contextual embeddings for accurate multilingual discourse segmentation of full documents[END_REF] at both granularities (sentence and document) used a sequential tagging model fine-tuned on contextual embeddings.

Multi-lingual discourse parsing is also becoming more popular, see for instance (Braud et al., 2017a;[START_REF] Chen | Modeling discourse structure for document-level neural machine translation[END_REF], in which it is seen as a form of multi-task learning problem, but this was not applied to discourse segmentation. In other NLP subfields, leveraging availability of corpora in different languages for the same tasks is an active area of research, with different strategies for combining tasks and languages, using meta-learning and complex sampling strategies [START_REF] Nooralahzadeh | Zero-shot cross-lingual transfer with meta learning[END_REF][START_REF] Tarunesh | Meta-learning for effective multi-task and multilingual modelling[END_REF]. A simpler approach that inspired us here, due to [START_REF] Dehouck | Phylogenic multi-lingual dependency parsing[END_REF], is to use the relations between close languages to guide the training process on a task: a generic model is trained on groups of languages, further refined with models by subgroups and finally fine-tuned on individual languages.

Data

The 2021 shared task provides 16 corpora annotated either with discourse boundaries (13) or discourse connectives in the case of PDTB corpora (3), with the RST Farsi corpus as a surprise dataset. This covers 11 different languages, mostly indoeuropean languages, and with a majority of european languages: 3 romance (Spanish, French, Portuguese), 3 germanic (English, German, Dutch), Russian, the only non indo-european being Turkish, Basque, and Mandarin. Some of the datasets depend on licences for the underlying text corpus, and are not freely available. We had licences for all of them except the Mandarin corpus (zho.pdtb.cdtb), provided by the organizers for the evaluation of the task. Except Farsi, all the datasets were present in the DISRPT 2019 shared task, but the russian Table 1: Descriptions of all corpora, according to the underlying theoretical framework. The tasks consist in finding connectives in the PDTB datasets, or the Elementary Discourse Units (segments) in RST and SDRT datasets. For each corpora are listed the number of documents in each split, the number of sentences and annotated units (connective tokens or segment boundaries in the training set, and whether the gold sentences were manually annotated or given by a parser.

dataset has been extended since, and some corpora without gold syntax annotations have been reparsed with Stanza or Spacy to provide morpho-syntaxic information for the sentence-internal subtasks.

All tasks are considered as sequence tagging, and annotated as such: for segmentation, each token is marked as being a segment boudary or not, and for connectives, which can span multiple tokens, the annotation follows the BIO convention with three labels Begin/Inside/Out for each token.

Datasets are not homogenous, as they were annotated along different principles based on three competing theoretical frameworks:

• Rhetorical Structure Theory [START_REF] Mann | Rhetorical Structure Theory: Toward a functional theory of text organization[END_REF], which assumes a linear segmentation of documents in discourse units (no overlaps), which are then related in constituant tree structures. This is followed in the majority of corpora (11).

• Segmented Discrouse Representation Theory [START_REF] Asher | Logics of Conversation[END_REF], which allows for embedded segments, and were linearized here for homogeneity of the task: a segment embedded in another one was re-annotated as forming 3 three segments. This is the case of two corpora.

• Penn Discourse Treebank [START_REF] Prasad | The Penn Discourse Treebank 2.0[END_REF], which annotates discourse connectives and their arguments in a discourse relation. This gives rise to a different annotation scheme as noted above, as the task is only to locate the connective.

Table 1 presents the size of all corpora, separated by theoretical framework, and expressed in number of documents, number of sentences, and number of discourse units (segments or connectives). Note that the different corpora greatly vary in sizes and annotations. One dataset is annotated on chat conversations (STAC), while all the others are on written text, mostly news or encyclopedic.

Experimental results cannot be compared to previous multi-lingual segmentation efforts (Braud et al., 2017b), because some of the corpora have been revised (Gum, RRT) or not taken entirely (CSTN), and some have been added (TDB, PRSTC), but should be quite close to the DISRPT 2019 evaluation, as only the Russian and the GUM corpora have been extended (and there is an additional dataset).

More details can be found about all datasets in the following publications: English RSTDT [START_REF] Carlson | Building a discourse-tagged corpus in the framework of Rhetorical Structure Theory[END_REF], PDTB [START_REF] Prasad | The Penn Discourse Treebank 2.0[END_REF], SDRT-STAC [START_REF] Asher | Discourse structure and dialogue acts in multiparty dialogue: the stac corpus[END_REF] and GUM [START_REF] Zeldes | The GUM corpus: Creating multilayer resources in the classroom[END_REF], Spanish RST (2) [START_REF] Iria Da Cunha | On the development of the RST Spanish Treebank[END_REF][START_REF] Cao | The RST spanish-chinese treebank[END_REF] Mandarin Chinese [START_REF] Zhou | Chinese discourse treebank 0.5 LDC2014T21[END_REF][START_REF] Cao | The RST spanish-chinese treebank[END_REF], German RST [START_REF] Stede | Potsdam Commentary Corpus 2.0: Annotation for discourse research[END_REF], French SDRT-Annodis [START_REF] Afantenos | An empirical resource for discovering cognitive principles of discourse organisation: the annodis corpus[END_REF], Basque RST [START_REF] Iruskieta | The RST Basque Treebank: an online search interface to check rhetorical relations[END_REF], Portuguese RST (Cardoso et al., 2011), Russian RST [START_REF] Pisarevskaya | Towards building a discourseannotated corpus of russian[END_REF], Turkish PDTB [START_REF] Zeyrek | Turkish discourse bank: Porting a discourse annotation style to a morphologically rich language[END_REF] Dutch RST [START_REF] Redeker | Multilayer discourse annotation of a Dutch text corpus[END_REF] and Persian RST [START_REF] Shahmohammadi | Persian rhetorical structure theory[END_REF].

Approach

In this paper we want to leverage combinations of multiple datasets for training, not only with corpora for the same language and task, but also with languages from the same families.

Base architecture

We started from the architecture that showed the best results on almost all languages and configurations at DISRPT 2019, namely [START_REF] Muller | ToNy: Contextual embeddings for accurate multilingual discourse segmentation of full documents[END_REF], which is built around BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF], a contextual language model that is easy to fine-tune on sequence tagging problems. The original architecture combined BERT contextual embeddings to the output of CNN filters over characters of each word piece, that were then fed to single-layer BiL-STM layer for the final prediction. The model is initialized with the multilingual BERT model, then fine-tune on all corpora separately as sequence tagging tasks. The original implementation used the AllenNLP library [START_REF] Gardner | Allennlp: A deep semantic natural language processing platform[END_REF], and so does our implementation.

Since BERT has a limitation on the number of word pieces it can take as input, a preprocessing step must be taken for document-level segmentation. In [START_REF] Muller | ToNy: Contextual embeddings for accurate multilingual discourse segmentation of full documents[END_REF], the core-nlp library was used to predict sentence boundaries, and use this information, while we used the more recent Stanza library by the same team for that purpose [START_REF] Qi | Stanza: A Python natural language processing toolkit for many human languages[END_REF].

We explored potential improvements for that architecture, swapping the multi-lingual pretrained language model XLM [START_REF] Conneau | Crosslingual language model pretraining[END_REF], or adding another layer to the BiLSTM stage. The final configuration was chosen based on preliminary experiments on some of the datasets, evaluated on their respective development sets.

They showed that XLM didn't help, but the extra layer of LSTM could. Changes to other hyperparameters didn't improve these preliminary results so we kept them as in the original model. Details of the parameters can be found in the declarative config file of the model, also added as supplementary material.

Input

Dataset grouping

Since the shared task involves multiple datasets with the same language (2 for Spanish RST, 2 for English RST), we assumed it would be beneficial to combine them for training. Datasets in the same language are not necessarily consistent in their annotation, but we hypothetize that they have enough commonalities to help training. We also took inspi-ration from work on multi-lingual syntactic parsing where a lot of corpora follow the same formalism, and where past work has tried to use commonalities between different languages, particularly the approach of [START_REF] Dehouck | Phylogenic multi-lingual dependency parsing[END_REF]

Results

Base model

The modification of ToNy, the best system from DISRPT 2019, gives us our base system on which we will build with multi-corpora training in a second stage.

We report the results of these systems on segmentation in Table 2, and on discourse connectives identification in Table 3, with precision, recall and F1 score on the detection of segment boundary tokens, and discourse connectives. A first comparison with respect to each best subsystem from 2019 for the 4 subtasks is given in Table 6. That means ToNy for segmentation (both intra-sentential and plain), discourse connectives (plain), and Gumdrop for discourse connectives (Conll input). We can see that on average on all datasets, the base system gains +0.5, mostly due to its improvements on the plain document segmentation (connective detection only involves 3 datasets). We left out the surprise dataset for 2021 from that evaluation, since we do not have a comparison point. Note that results on this new dataset are good and consistent with the other corpora. Lower results are obtained on smaller datasets for obvious reasons (Spanish sctb, Chinese Mandarin sctb, and to a lesser extent Basque and French). Models trained without sentence information perform a little worse, as expected, with -1.6% on average, again with wider gaps for small corpora.

We do not show the breakup by dataset for the comparison with DISRPT 2019, but there is a lot of variances in results, with differences ranging from -4.5 (French Annodis) to +6.85 (Mandarin SCTB), and not necessarily only on small corpora. 4: Intra sentential results on romance development datasets, with different training setups: SPA means the grouping of both spanish datasets for training, SPO the grouping of spanish and portuguese data, ROM the addition of French to the group. FT means a model fine-tuning the SPO model. Lines with "self" are just copied from the basic evaluation (training on the dataset only) for comparison. In bold are indicated the best F1 results per dataset on their development set, and the corresponding model was thus kept for the final evaluation.

Corpus

Multi-dataset training

As shown above, a lot of smaller datasets have lower results than larger ones, which is to be ex-pected. We present here the result when applying the strategy described in Section 4.2. We tried it on two groups of languages: romance languages, and germanic languages.

For romance languages, since there are two spanish RST corpora, we grouped them to trained a "spanish" more generic model, then we trained a model with all Spanish and Portuguese data, then a generic romance model by including also French. We then used those models for predictions on the datasets respective development part. We did something similar with germanic languages, grouping all English datasets into one, joining the Dutch and German datasets into another one, and finally training a generic germanic model on all of them. Following a procedure similar to what was done in [START_REF] Dehouck | Phylogenic multi-lingual dependency parsing[END_REF], we also fine-tuned some of these models on the individual datasets before using them for prediction. Lack of time during the campaign prevented us from trying all combinations and all datasets like this, but we tested this on all Spanish and English datasets, respectively fine-tuning the global Spanish-Portuguese on Spanish and Portuguese datasets (since it showed a good compromise on the dev sets) and the global English model on all English datasets. Due to time constraints, we tested this only on one type of input, the sentence level (conll files).

Results are presented in Tables 4 and5. For the final evaluation, we kept for each dataset the model that performed better on the dataset development test.

Final evaluation

For the final evaluation of the campaign, every team provided their code and instructions for reproducing the experiments, and one member of the organization team reproduced entirely the experiments of one model they were not involved with (two of the four teams involved organization members, including the present system).

We reported the official scores on the test sets in Tables 7 for segmentation and 8 for connective detection.

Overall our system is ranked 3rd out of 4, with results very close to the 2nd-ranked system (Segformers), with only 0.15% difference on average for treebanked data segmentation, and 0.45% on plain data segmentation. The gap with the first ranked system (DiscoDisco) is 0.7% on average on treebanked segmentation and 1.28% on plain documents. We have the best scores on these languages, but note that cross-training cannot really explain the good results on German, since results are surprisingly similar between treebanked and plain data.

Conclusion

We presented an approach for discourse segmentation and discourse connective identification, both at the sentence and document level, in a multi-lingual and multi-formalism context. Building on the successful architecture from the 2019 DISRPT shared task, we leverage datasets in the same or similar languages to augment training data and improve on the best systems from the previous campaign, on 3 of the 4 sub-tasks. While below the best system which uses a rich set of features over a similar architecture, we still manage to have the best scores on some of the languages where we experimented with cross-lingual training: German and Spanish for sentence-internal segmentation. Due to time constraints, we could not fully explore all potentially useful language combinations and fine-tuning on specific datasets, that could help improve on the tasks, and give insights on how different languages help each other addressing the discourse segmentation problem. Further progress on multi-lingual embeddings or alignments of different embeddings could be a source of future investigations, as well as more elaborate multi-lingual training procedures.

Table 2 :

 2 Segmentation results on the development sets, for both sentence (conll) and document (doc) levels.

		Corpus	P	R	F1
		deu.rst.pcc	92.58 95.27 93.91
		eng.rst.gum	94.06 90.19 92.08
		eng.rst.rstdt	96.35 95.38 95.86
		eng.sdrt.stac	94.19 95.49 94.84
		eus.rst.ert	87.23 83.75 85.46
		fas.rst.prstc	91.18 91.49 91.33
	conll	fra.sdrt.annodis 87.13 90.11 88.59 nld.rst.nldt 95.52 93.29 94.40
		por.rst.cstn	90.63 92.06 91.34
		rus.rst.rrt	86.04 83.83 84.92
		spa.rst.rststb	91.80 93.56 92.67
		spa.rst.sctb	85.57 80.58 83.00
		zho.rst.sctb	93.02 77.67 84.66
		mean	91.18 89.44 90.24
		deu.rst.pcc	94.51 93.82 94.16
		eng.rst.gum	91.80 91.68 91.74
		eng.rst.rstdt	93.48 94.94 94.20
		eng.sdrt.stac	86.10 87.52 86.81
		eus.rst.ert	87.56 85.23 86.38
		fas.rst.prstc	91.21 91.84 91.52
	doc	fra.sdrt.annodis 87.52 90.83 89.14 nld.rst.nldt 93.91 94.46 94.19
		por.rst.cstn	92.43 91.11 91.77
		rus.rst.rrt	83.09 81.65 82.37
		spa.rst.rststb	92.54 94.75 93.63
		spa.rst.sctb	73.23 90.29 80.87
		zho.rst.sctb	64.18 83.50 72.57
		mean	87.04 90.12 88.41

Table 3

 3

	: Connective identification results on the devel-
	opment sets, for both sentence (conll) and document
	(doc).

Table

		Group	P	R	F1
		self	91.80 93.56 92.67
	spa/rststb	SPA SPO 93.81 94.03 93.92 94.24 93.79 94.02
		ROM 93.66 91.65 92.64
		FT	94.30 94.75 94.52
		self	85.57 80.58 83.00
	spa/sctb	SPA SPO 86.24 91.26 88.68 83.64 89.32 86.38
		ROM 81.98 88.35 85.05
		FT	88.89 85.44 87.13
		self	90.63 92.06 91.34
	por/cstn	SPO 92.88 89.05 90.92
		ROM 90.14 90.00 90.07
		FT	90.98 92.86 91.91
	fra/annodis	self ROM 91.12 83.09 86.92 87.13 90.11 88.59

Table 5 :

 5 Intra sentential results on germanic development datasets, with different training setups: GD means the grouping of German and Dutch for training, GER the grouping of English, German and Dutch,

	and ENG the grouping of all 3 English datasets. FT
	means a model fine-tuning the global ENG model on
	the specific corpus training set. Lines with "self" are
	just copied from the basic evaluation (training on the
	dataset only) for comparison. In bold are indicated the
	best F1 results per dataset on their development set.
	text segmentation. Our system performed less well
	on connective detection, especially with respect to
	models taking dependency between labels into ac-
	count (such as a CRF in the case of DiscoDisco):
	about 4.5% less than Segformers and 6% less than
	DiscoDisco, mostly due to lower results on the
	Mandarin dataset. 3
	It is to be noted that we achieved our best results
	in relation to the other systems with datasets used in
	cross-training with similar languages (see Sections
	4.2 and 5.2), and for which we observed on the
	development data that it had an impact: German
	and Spanish corpora, in the case of treebanked data
	(conll), since we didn't have time to try this strategy

Table 6 :

 6 Mean comparison of our base system and our improved system with respect to the best Disrrpt 2019 system for each sub task, and the mean on all 16 datasets. This is the only evaluation we made on the test set prior to the official evaluation. Note that grouped training was tested only on conll segmentation, so the other scores are just copied from the base system.

Table 7 :

 7 Final official segmentation results on the test set, reproduced by the organizers. In bold, F1 scores for which our system has the best performance of the shared task.

	treebanked	P	R	F1
	deu.rst.pcc	98.91 92.52 95.61
	eng.rst.gum	93.27 93.65 93.46
	eng.rst.rstdt	96.16 95.99 96.08
	eng.sdrt.stac	97.41 92.37 94.82
	eus.rst.ert	90.04 83.11 86.44
	fas.rst.prstc	93.54 90.75 92.12
	fra.sdrt.annodis 87.26 88.67 87.96
	nld.rst.nldt	94.15 95.27 94.71
	por.rst.cstn	90.31 94.44 92.33
	rus.rst.rrt spa.rst.rststb	88.19 81.10 84.50 92.04 93.04 92.54	treebanked	P	R	F1
	spa.rst.sctb	85.39 90.48 87.86	PDTB	93.32 88.67 90.94
	zho.rst.sctb	92.48 73.21 81.73	TDB	90.55 86.93 88.70
	mean	92.24 89.58 90.78	CDTB	84.43 66.03 74.10
	plain	P	R	F1	mean	89.43 80.54 84.58
	deu.rst.pcc	94.67 96.60 95.63	plain
	eng.rst.gum	92.76 89.54 91.13	PDTB	88.84 92.09 90.43
	eng.rst.rstdt	93.39 94.50 93.94	TDB	90.12 88.10 89.10
	eng.sdrt.stac	85.30 87.01 86.14	CDTB	77.40 72.44 74.83
	eus.rst.ert	91.45 83.78 87.45	mean	85.45 84.21 84.79
	fas.rst.prstc	93.59 89.40 91.45
	fra.sdrt.annodis 89.90 86.41 88.12
	nld.rst.nldt	94.35 93.79 94.07
	por.rst.cstn	93.36 91.83 92.59
	rus.rst.rrt	83.60 84.01 83.80
	spa.rst.rststb	92.19 89.78 90.97
	spa.rst.sctb	78.65 89.88 83.89
	zho.rst.sctb	68.11 75.00 71.39
	mean	88.56 88.58 88.51

Table 8 :

 8 Final official connective detection results on the test set, reproduced by the organizers.

Note that authors Philippe Muller and Chloé Braud were part of the organization of the shared task.

https://gitlab.irit.fr/melodi/ andiamo/discoursesegmentation/discut

Full results for all systems are not shown for space constraint reasons, but are displayed on the Shared task website at https://sites.google.com/georgetown. edu/disrpt2021/results and are summarized in the introductory paper to the Shared Task proceedings.

Acknowledgments

This work was partially supported by the ANR (ANR-19-PI3A-0004) through the AI Interdisci-plinary Institute, ANITI, as a part of France's "Investing for the Future -PIA3" program, and through the project SLANT (ANR-19-CE23-0022) and Quantum (ANR-19-CE23-0025).