dataesr/scientific-paragraphs-categorization huggingface dataset:
As observed in the experimental 3D structures that can serve as templates for homology modeling (pdb entries 1yo8 and 3fby), TSP repeats are folded domains with calcium ions bound into the core through acidic (aspartate) residues. The foldable segments delineated here contain conserved cysteine residues that form interdomain disulfide-bridges, providing tight interactions in the wire architecture typical of the TSP-2 signature domain  [48]. 2  for the technical flow), as follows: percentage of segment residues participating in a regular secondary structure (RSS), percentage of segment residues accessible to the solvent (Accessibility), percentage of segment residues predicted to be disordered (Disorder), the mean number of BFD homologs per segment residue (Known homologs). The binary conditions based on each feature threshold are indicated on the edges of the tree (for details, see Section 2).
Supplementary Figure  S2  provides details of the HCA plots of the foldable segments whose 3D structures are shown in Figure  4. The folded domains contain ~1/3 strong hydrophobic amino acids distributed in clusters, which correspond to the positions of RSS. A significant number of cases also exist with a smaller number of BFD homologs (296 segments, Figures  3  and 4 (d2)). Here, the consideration of experimental 3D structures as templates can explain the accurate AF2 prediction (pdb:1sed for the example shown in Figure  4 (d2)). Other interesting cases are those of folded domains corresponding to sequences predicted to be disordered for a large part, but which are clearly not (Figure  4 (c1,c2) corresponding to histone fold, 29% identity with pdb 2lso-A, and to a case with no obvious similarity with known 3D structures, respectively).
Full-VL Segments with AF2 Well-folded Models The category that is most populated for full-VH segments, i. e. , 3D models with low solvent accessibility and tight contacts between the RSS, accounts for a substantial number of full-VL cases, although not predominant (293 segments: Figure  5 , blue box). These AF2 predictions correspond to well-folded 3D structures, as illustrated with the yeast uncharacterized protein YBR032W (UniProt P38223, Figure  7b , blue box). This was predicted as an alpha + beta fold, but no significant structural similarity could be detected in the PDB database by the Dali server. The four levels of the tree (from the root on the left to the last internal nodes on the right) correspond to the four features describing the segments (see Figure  2  for technical flow), as follows: percentage of segment residues participating in a regular secondary structure (RSS), percentage of segment residues accessible to the solvent (Accessibility), percentage of segment residues predicted to be disordered (Disorder), mean number of BFD homologs per segment residue (Known homologs).
The 3D structure at right illustrates the AF2 prediction for a member of the same family as the protein sequence shown on the left. The blue box corresponds to the sequence included in the leaf that is the most populated in the full-VH tree shown in Figure  3. Subfigures Logically, about five times as many cases are found with a low number of BFD homologs (1274 segments: Figure  5 ). This reinforces the observation that while assigning a low confidence score, AF2 can propose models even when little evolutionary information is available (Figure  7c, d). A first example (UniProt A0A1I9LP79, Figure  7c ) corresponds to an uncharacterized protein from Arabidopsis thaliana, whose 3D structure is predicted as a 12-stranded beta-sandwich. A Dali-server search in the PDB database revealed multiple hits with similar structures but with a lower strand content (Z-scores up to 6.
6 and sequence identities below 15% (e. g. , pdb:4q7g-A, Z-score of 6. 6, 8% identity)). Examination of the HCA plot indicated that all the hydrophobic clusters match the regular secondary structures predicted by AF2. This suggests that the basic secondary structure elements are indeed present in the proposed model, arranged correctly or not. However, no conclusion can be drawn in the absence of a sufficient number of homologs (mean BFD homologs per position: 5. 08, mean sequence identity > 60%). A second intriguing example is an uncharacterized protein from Trypanosoma cruzi (Q4CUB3), consisting of a repeated motif of 70 amino acids (mean BFD homologs per position: 10. 16, identity > 80%) (Figure  7d ). This is predicted to form a repeated beta-alpha-beta-alpha motif, with the two helices arranged on either side of a central beta sheet of parallel beta-strands, forming an elongated structure with a continuous hydrophobic core.
A Dali search revealed structural alignments with different tandem-repeat structures (Z-scores up to 4. 4, with sequences identity below 10%), belonging to distinct structural families (armadillo repeats (pdb:6dee-A, Z-score: 4. 3, 7% identity), right-handed beta-helix (pdb:5zru-A, Z-score: 4. 1, 3% identity; 1bhe-A, Z-score: 4. 1, 5% identity), heat repeats (pdb:5loi-A, Z-score: 4. 0, 9% identity)). In addition, AF2 predictions made for some homologous sequences correspond to a different repeat fold, always predicted with a low to very low level of accuracy (e. g. , Q4CW36_TRYCC, >80% mean identity on the repeated sequences, AF2 prediction corresponding to a right-handed beta helix, at right on Figure  7d ). This suggests that this repeat module may correspond to a novel 3D structure, which deserves to be explored experimentally.
A third example (UniProt Q8WU49, Figure  7a ) illustrates a case containing amino acids predicted to be disordered, in contrast to the former. It corresponds to the uncharacterized human protein C7orf33, which is taxonomically restricted to primates (mean BFD homologs per position: 4. 49, mean identity 76%). The 3D structure predicted by AF2 corresponds to a beta-sandwich, with seven strands. A Dali search yielded many results with similar structures (Z-scores up to 5. 9 and sequence identities below 15% (e. g. , pdb:6eon-A, Z-score 5. 7, 8% identity)). Examination of the HCA plot indicated that not all the hydrophobic clusters present in the sequence correspond to the regular secondary structures predicted by AF2. Instead, there are at least five hydrophobic clusters that correspond in the AF2 model to large, unstructured coils.
Nevertheless, it cannot be ruled out that AF2 fails to predict RSS that can assemble into stable, well-folded 3D structures due to the lack of evolutionary information (or, for cases with a high number of BFD homologs, to insufficient depth of multiple sequence alignments). Such cases are referred to as "hidden" (unconditional) order. These hypotheses of conditional or unconditional order cannot be unequivocally demonstrated without the use of experimentation. Nevertheless, we give below some examples supported by experiments that confirm these hypotheses. The first category (conditional order) is further supported by the fact that some instances are annotated in the DisProt database (Figure  8 , green box). This is illustrated by a first example (Figure  8c ) corresponding to a foldable segment of the mouse glucocorticoid receptor (GCR, UniProt P06537), including its core transactivation domain (DisProt DP00030, 94.
A foldable segment (aa 670-728, HCA score: 0. 62, IUPred2 coverage 100%) with three hydrophobic clusters typical of an alpha-betaalpha motif can be found in its large, otherwise, intrinsically disordered cytoplasmic domain (Figure  8d ), for which a role in signaling has been suggested but this function has yet to be elucidated  [55]. The foldable segment highlighted here is a good candidate for further exploration of conditional order, even though this remains to be supported at the experimental level. Short linear motifs (SLiMs)  [56]  are a priori excluded from this study because their lengths are below the threshold fixed here (30 amino acids) and as they often contain only a single hydrophobic cluster  [30]. Such cases are associated with higher HCA scores (Bruley et al. [32] ). However, some SLiMs can be embedded in larger foldable segments  [30] , allowing their detection in the present dataset.
The long, soluble-like full-VL foldable segments studied here may correspond to (i) cases of induced folding without the formation of a folded domain, resulting from the interaction of individual regular secondary structures with a partner, (ii) cases where a folded 3D structure is formed, dependent on the partner to be induced/stabilized, (iii) cases where a folded 3D structure is stably formed, independent of the environment (what we designate as unconditional, hidden order). This unconditional order remains completely invisible in AF2 predictions, presumably due to the lack of homologs or insufficient depth of the multiple sequence alignments used in the machine learning process. While cases of conditional order can be supported by taking into account the DisProt database, this is not obvious for cases of hidden, non-conditional order.
g. ,  [60] ) but also for 3D structure prediction from single protein sequences without known homologs (e. g. ,  [61] , based on the protein language model) will thus open new perspectives to decipher these cases. The distinction between conditional and hidden, non-conditional order is not straightforward, but can be guided by taking into account current disorder predictors, in particular integrating more information on the amino acid composition. Useful information could also be given by the hydrophobic cluster composition (e. g. , based on the HCA toolkit), as well as by sequences linking the hydrophobic clusters, which correspond mainly to loops. Several hypotheses can explain the low confidence scores associated with the folded AF2 model segments. First, the proposed 3D structures should be adopted but are not yet validated by AF2 due to either: original folds/structures, the lack of representation in the databases used for learning, or an insufficient amount of homologous sequences to validate the predicted contacts.
In this paper, we develop numerical tools to analyse the perturbative stability of classical flux compactifications, and apply them on a database of such solutions. We focus in this work on solutions of 10-dimensional (10d) type IIA/B supergravities, with 4d maximally symmetric spacetimes. Those are candidates to be classical string backgrounds; whether or not they are in the classical string regime remains to be verified, but this does not affect the results of this paper. For these 10d solutions, we follow the ansatz and conventions of  [15] : the 6d space is a group manifold (whose compactness is a priori not ensured, but analysed in detail in  [5] ), the fluxes have constant components in the left-invariant basis, and the only extended objects included are D p -branes and orientifold It describes 4d scalar fields ϕ i minimally coupled to gravity and subject to a scalar potential V.
These fields can be understood as fluctuations around the 10d solutions, and as such they capture some of their (in)stability. More precisely, the 10d solutions will turn out to correspond to critical points of the potential (loosely referred to as extrema in the following), i. e. points in field space where ∂ ϕ i V = 0 ∀i. The stability is then captured by the (sign of the) eigenvalues of the Hessian of the potential, related to those of the mass matrix, as we will explain. This led in  [5]  to analyse the stability of solutions by considering a restricted set of fields, (ρ, τ, σ I ), first introduced in  [23] , corresponding to some combinations of diagonal metric fluctuations and the dilaton. This analysis had been automated and performed with the code MaxSymSolSpec (MSSSp). As in any dimensional reduction, a fundamental aspect is the truncation: the 10d fields, developed on an infinite basis of 6d modes, need to be truncated to a finite set, whose physics will be described by the 4d theory.
In this work, we will perform consistent truncations: as we will recall, finding an instability within this set of modes is sufficient to conclude on the instability of the 10d solution. Although phenomenologically debatable, this truncation will then be enough for our purposes. We implement it, as well as the corresponding dimensional reduction and resulting 4d theory, in an automated fashion in the code MSSV. Proving that a truncation is consistent is challenging. It first requires to find an appropriate truncation ansatz, and then verify that all 4d equations are captured by 10d equations. As we will review in section 2. 1, it remains expected that the truncation of the 10d fields to left-invariant fluctuations on group manifolds is a consistent truncation, even in presence of (smeared) O p /D p sources.
The resulting theory is expected to be a 4d gauged supergravity. But this has typically been verified in a case by case analysis, for various compactifications and source configurations. In this work, thanks to a detailed comparison between the 10d equations given by the code MSSS  [15]  and the 4d equations provided by the new code MSSV, we prove for 4d maximally symmetric spacetimes that the truncation to left-invariant scalar fields on group manifolds is consistent for all 21 solution classes of  [15]  in type IIA/B, corresponding to various O p /D p source configurations. We actually get more: we show a perfect matching between 10d and (combinations of) 4d equations of motion, with the same amount of equations on both sides. This means that there is actually no extra degree of freedom in the 10d ansatz (even though there are more constraints to satisfy in 10d).
1). We give in particular the scalar potential including the axions in equations  (2. 19 ) and (2. 20). We also discuss the computation of the scalar fields' kinetic terms. We can then motivate and define the mass matrix and the η V parameter, to be used in stability studies. The truncation, dimensional reduction and stability analysis are then implemented in the code MSSV, presented in section 3. A first use of this code is then the verification in section 4 that we have a consistent truncation of our 10d starting point. This is achieved thanks to a comparison of 10d and 4d equations of motion, as explained previously. Note that both codes, MSSS and MSSV, and both papers have compatible conventions. This could allow to use them further together, for instance MSSS for the search of solutions and MSSV to study the stability.
We turn in section 5 to analysing the stability of the previously mentioned solution database. We start by determining and discussing in section 5. 1 the generic flat JHEP12(2022)026 directions in each of the 21 solution classes. Those appear as massless modes in the spectrum of 10d solutions. We then study the spectrum and stability of de Sitter solutions in section 5. 2, Minkowski solutions in section 5. 3 and anti-de Sitter solutions in section 5. 4. We comment on the results and compare them to corresponding swampland conjectures. Finally, we summarize our findings in section 6 and provide an outlook.
Dimensional reduction on group manifolds In this section, we review the details of type II flux compactifications on group manifolds in the presence of orientifolds and D-branes. Our starting point is the low-energy limit of type II string theories, namely 10d type II supergravities with the actions as given in  [24]. We first present in section 2. 1 the truncation of 10d fields, commonly followed when compactifying on 6d group manifolds. We then use it in section 2. 2 to perform the dimensional reduction from 10d to 4d, with a focus on scalar fields and their scalar potential V. This reduction is implemented in the code MSSV described in section 3, and further used in section 5 to study the 4d stability of 10d compactifications.
One can then consider the mass matrix M in the canonical basis, of coefficients M i k = δ ij ∇ ĵ ∂ kV. One can verify that M = P M P -1 = δ -1 P -T ∇∂V P -1 , where the matrix ∇∂V computes the Hessian of V in the non-canonical field basis. We will use these formulas to get our spectrum data. Indeed, the code MSSV first computes the matrix P using the relation (K ij ) = P T δP , and introducing an orthonormal matrix O and a diagonal one D, such that P = D -1 O. Then, the mass matrix is computed with M = δ -1 P -T ∇∂V P -1. From there, its eigenvalues and eigenvectors are determined. An eigenvector can be expressed as v = v i ∂ φi , and we store the coefficients v i as columns in a matrix. Expressing the eigenvectors in the non-canonical basis (to understand their field directions) then amounts to using the relation ∂ φ = ∂ ϕ P -1.
The code MSSV: tutorial In this section, we briefly present how the code MSSV works (available as supplementary material), and provide a few useful commands. MSSV stands for Maximally Symmetric space-JHEP12(2022)026 time Solutions V , where V refers to the complete scalar potential V obtained via the dimensional reduction described above. The code has been developed Wolfram Mathematica 13  [63]. MSSV takes as input the source configuration corresponding to a certain solution class of  [15] , meaning the number of O p -planes, of D p -branes, and the directions along which they are placed. This is also referred to as the "model", since this data determines the 4d theory and its field content. Once executed, the code begins by using the user's input to find the left-invariant scalar fields and the background fluxes after the orientifold projections.
The code then computes, following section 2, the 4d kinetic terms and scalar potential for these fields and fluxes and packages them as per equation (2. 9). The code also determines those of the scalar fields that are generic flat directions, as discussed in section 5. 1. In the code we have set M p = 1. The next required input is that of a concrete 10d solution obtained from the code MSSS and listed in the accompanying database  [15]. This amounts to assigning values to all the fluxes appearing in the variable fluxes. Through the command AnalyseSol, after performing a few checks on the 10d solution, the code is then able to extract the mass spectrum and the η V value (see equations (2. 23) and (2. 24)). It also provides the mass matrix eigenvectors for the tachyonic and massless modes. In the case of multiple massless modes, the corresponding eigenspace is degenerate and the code chooses a random basis in field space that spans it.
Note that the computation of the mass spectrum by the code assumes to be at a critical point, where ∂ ϕ i V = 0, axions (including off-diagonal metric components) vanish, and diagonal metric components as well as e φ are set to one. All models analysed below do correspond to critical points. In order to calculate the kinetic terms, the potential value, V and η V at a generic point in field space, the user has to call AnalysePointGen. To run this command, the user must assign values to the background fluxes as well as to the scalar fields. We now list a few useful commands; more are provided in the code. • RunModel -Initializes the model, then prints out the left-invariant scalar fields and background fluxes for the chosen source configuration along with any generic flat directions, i. e. left-invariant scalar fields that generically do not appear in V.
JHEP12(2022)026 • V -Returns the scalar potential as a function of the flux parameters defined in the variable fluxes and evaluated at the critical point defined in the variable extremum. The two most useful commands are RunModel and AnalyseModel, which must be evaluated before calling on the other commands. Finally, let us mention that the notebook allows to analyse different source configurations as well as several solutions, without having to quit or restart it. Indeed, the main part of the code is run once and for all, and one can then just call commands, or redefine the input. This allows in particular the user to evaluate once a whole notebook where many solutions have been entered to be analysed.
Stability analysis Stability of solutions with maximally symmetric spacetimes is at the heart of several swampland conjectures, as recalled in the Introduction; it also plays an important role for phenomenological models. In this section, we use the 4d theory discussed in section 2 and the corresponding code MSSV described in section 3 to study the stability of the de Sitter, Minkowski and anti-de Sitter solutions found in  [15, 21, 22]. The solutions database can be found in two files provided with  [15]. These solutions were found with the code MSSS  [15]  which is compatible with the present code MSSV. The conventions of  [16, 58]  followed in  [15]  are the same as in the present paper, and we verify in particular that these solutions are critical points of the scalar potential V obtained here, satisfying ∇V = 0 as JHEP12(2022)026 well as V = M 2 p 4 R 4.
This is actually formally ensured thanks to the analysis described in section 4 regarding consistent truncations. The stability of these solutions has already been analysed using MSSSp in  [5] , considering only the 4-6 scalar fields (ρ, τ, σ I ) corresponding to some dilaton and diagonal metric fluctuations. Thanks to the above dimensional reduction, embedded in the code MSSV, we now have a complete set of scalar fields, a corresponding scalar potential as well as kinetic terms. This allows us here to provide a more complete analysis of the perturbative stability of these solutions. The latter will essentially be discussed in terms of the parameter η V defined in  (2. 24) , or the spectrum of masses 2 , which are the eigenvalues of the mass matrix  (2. 23). Both are evaluated at the critical point of the potential, corresponding to the solution, where the axions and off-diagonal metric components vanish, while the diagonal ones and the exponential of the dilaton are equal to one.
JHEP12(2022)026 We first describe in section 2. 1 our truncation of the 10d fields, which consists in keeping the left-invariant scalar fields on the group manifold. As discussed there, those are not guaranteed to be the lightest fields (for generic group manifolds) but they are providing a consistent truncation before orientifolding  [36]. It is expected that the same still holds after including orientifold planes, as shown in various examples. In section 4, we prove explicitly that our truncation is consistent for all 21 solution classes of  [15] ; let us recall that these compactifications include orientifolds. To reach this result, we compare the 10d equations of motion provided by the code MSSS  [15]  and the 4d equations given by MSSV at extrema. Even though a consistent truncation may differ from a low energy truncation, it is sufficient for our purposes when studying the stability of solutions and finding an instability.
Based on this truncation, we derive in section 2. 2 a corresponding 4d theory starting with 10d type II supergravities with O p /D p sources. We get in particular the scalar potentials in equations  (2. 19 ) and (2. 20), and compute the scalar kinetic terms. Those allow to define the mass matrix in equation (2. 23), that will provide us with the 4d mass spectrum. This derivation is automated in the code MSSV, a Mathematica  [63]  notebook presented in section 3. This code further computes the mass spectrum for a given solution and related quantities characterising stability. This code is then used in section 5. 1 to identify generic flat directions in the various solution classes, that would appear as massless modes in the spectrum. We finally turn in section 5. 2, 5. 3 and 5. 4 to the stability analysis of 10d solutions with 4d de Sitter, Minkowski or anti-de Sitter spacetimes, respectively.