dataesr/scientific-paragraphs-categorization huggingface dataset:
We obtained 69 species for the construction of a core genome-based phylogeny using closed genomes or, if not, the draft genome for each species (Figure  1 ). Phylogeny results were similar to a recently published study  (Chen et al. , 2021). Of note, although most genomes available in the NCBI database originated from coccoid Neisseria (lineage 1; dark blue in Figure  1 ), the detailed phylogenetic analysis of this lineage, which likely evolved from an ancestral rod  (Veyrier et al. , 2015)  and which include the well-known pathogens N. meningitidis and N. gonorrhoeae, will be presented elsewhere  (Veyrier lab, in preparation). Using Scanning-Electron Microscopy (SEM), we imaged all the species that are available in public collections to morphologically classify them as rod, cocci or MuLDi.
Downregulation of dcw cluster genes in MuLDi Neisseriaceae As several genes encoding for regulators were mutated in MuLDi, we employed RNAseq to determine differential gene expression patterns between MuLDi (n=5) and rod-shaped (n=5) Neisseriaceae cultured in the same condition (GCB agar Media, 6h, 37°C 5% CO 2 ). To compare gene expression between species, we standardized the annotation of the ve rod-shaped and the 5 MuLDi Neisseriaceae genomes by inferring gene orthology using BlastP. Using NetworkX python programming package  (Hagberg et al. , 2008) , we reannotated clusters of homologous genes in each genome (for example, ftsZ gene will be called NEISS_1241 in all the genomes). By doing so, we were able to count the reads associated with each gene in each species and perform DESeq2 statistical analyses using the core transcriptome.
coli, MraZ is described as a transcriptional repressor that controls its own expression and that of other dcw cluster genes  (Eraso et al. , 2014). Importantly, deletion or overexpression of MraZ led to cell lamentation in bacteria where MraZ, respectively, activates (e. g. , Mycoplasma spp. ) or represses (e. g. , E. coli) the dcw cluster. If downregulation of the dcw cluster did not result in N. elongata lamentation, its upregulation, in MraZoverexpressing N. elongata, led to shorter cells. Altogether, our data suggest that, in the Neisseriaceae, MraZ is controlling cell elongation via the regulation of the dcw cluster and we speculate that it may have altered the balance between the divisome and the elongasome machineries (i. e. , in mraZ-less MuLDi, the elongasome might contribute to PG synthesis in the septum).
Fluorescence microscopy For Figure  2  and Supplementary Figures  S1  and S4  immunostained or FDAA-labelled bacteria were imaged using a Nikon Eclipse NI-U microscope equipped with a MFCool camera (Jenoptik) and images were acquired using the ProgRes Capture Pro 2. 8. 8 software (Jenoptik). For Figure  3  and Supplementary Figure  S5 , FDAA-labelled bacteria were visualized with a Leica TCS SP8 X confocal laser scanning microscope. Images were taken with a 63X Plan-Apochromat glycerine objective with a NA of 1. 30 and a refraction index of 1. 46 (glass slide, glycerine and antifade mounting medium). The Leica software LASX (3. 7. 2. 22383) was used for image acquisition and post-processing if necessary. For Figure  6  and Supplementary Figure  S8 , FDAA-labelled N. elongata wild type (rpsL*) and mutant (rpsL*; cdsA-amiC SM ; mreB SM ) were imaged at the INRS-CAFSB platform with a Zeiss LSM 780 AxioObserver confocal microscope equipped with a Zeiss Plan-Apochromat 100x/1.
FDAA uorescence quanti cation and statistical analysis Microscopic images were processed using the public domain program ImageJ  (Schneider et al. , 2012)  in combination with plugin Fil-Tracer (this study). Cell outlines were traced and morphometric measurements recorded. Fluorescent intensities were measured along the septal plane and plotted as fraction of the normalized cell length. Automatic cell recognition was double-checked manually. For representative images, the background subtraction function of ImageJ was used and brightness and contrast were adjusted for better visibility. Data analysis was performed using Excel 2021 (Microsoft Corporation, USA), plots were created with ggplot2 in R (http://www. R-project. org/). Septa length (Figure  6  and S8) of BADA and TADA labelled cells were analysed using the public domain software Fiji  (Schindelin et al.
The base call was carried out using guppy_basecaller (version 5. 0. 11+2b6dbff) in sup mode. Reads were ltered by quality Q> 8 and separated by barcodes using guppy_barcoder (version 5. 0. 11+2b6dbff). The genome assembly was made by 3 programs: Canu Neisseria elongata subs. glycolytica ATCC 29315 (bacilli, accession number GCA_000818035. 1) as references. The proteins encoded in each genome under study here were further compared against these two references by TBLASTN. Once the blast results were obtained, and the groups to be compared were de ned, i. e. multicellular versus bacilli, amino acid changes in proteins shared by both groups (identity threshold 60%) were investigated. In this regard, CapriB has several analysis options, but the study focused on those amino acids that remain identical in the members of one group but are modi ed in the other (I vs D option).
1. 5). Paired FastQ reads were then aligned against Neisseria elongata subsp. glycolytica ATCC 29315 (accession number NZ_CP007726. 1) genome using Bowtie2 (Version 2. 4. 2) and read counts were determined using htseq_count (Version 0. 9. 1) tool. Subsequently the gene expression of the transcripts was determined using DESeq2  (Version 2. 22. 40. 6 ). Visualization of differentially expressed genes was done with Venn diagrams, drawn by a Web-based platform Venny 2. 1 (https://bioinfogp. cnb. csic. es/tools/venny/). For intra-genus transcriptomic comparison presented in Figure  8 , rRNA depleted mRNA were treated using the RevertAid RT Reverse Transcription Kit (K1691; Thermo Scienti c™) with some adjustments. For rst strand cDNA synthesis, 1 ul of random primer (3 μg/μL ; 48190011; Invitrogen™) was added and the solution was incubated at 65°C.
Network connection was thereafter established with the python programming package NetworkX version 2. 6. 2  (Hagberg et al. , 2008)  with a cut-off of 60% of similarity. Basically, all proteins showing more than 60% similarities with Coordinates of the dcw cluster and of the cdsA loci were obtained by tblastn for each Neisseriaceae genome. Once the genomic location of each sequence was determined, the sequences were extracted using tools available in the EMBOSS package  (Rice et al. , 2000). The resulting sequences were annotated with Prokka, and the output gbk les were used to construct the synteny by employing EasyFig 2. 2. 2  (Sullivan et al. , 2011).
M. N. was funded by a postdoctoral fellowship from the Swedish Society for Medical Research (SSMF). Y. V. B. is also supported by a Canada 150 Research Chair in Bacterial Cell Biology. F. J. V. received a Junior 1 and Junior 2 research scholar salary award from the Fonds de Recherche du Québec -Santé. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
ACKNOWLEDGEMENTS The authors are extremely grateful to  Markus Christian Schmid  and the  Division of Microbial Ecology of the University of Vienna  for providing the confocal microscope and technical support with the imaging. P. M. W. is grateful to  B. Bejtovic  for preliminary experiments. We thank  Nathan Weyand  for providing us N. sp. DentCa1247. We thank  Tanneke den Blaauwen  of the  University of Amsterdam  for inspiring and constructive discussions.
Molecular dynamics simulation The RBD structure of the SARS-CoV-2 S protein complexed with the hACE2 PD was obtained from the Protein Data Bank (PDB) with PDB id 6LZG  23. The missing residues of this WT structure were added by the CHARMM-GUI webserver. Four glycans are located at residues 53, 90, and 322 of the hACE2 PD and at residue 343 of the viral RBD. In this work, we adopted two glycan schemes that were created using the CHARMM-GUI web server. In a homogeneous setup, all glycans are of the same type, while in a heterogeneous setup, glycan sites have different glycans  24, 25. The Omicron variant was generated from WT RBD using the CHARMM-GUI webserver. In total we have 4 complexes with 2 sets of glycans for each variant. The Zn ion in hACE2 PD of the original structure was retained.
The original structures for WT and Omicron are shown in Figure  1. All mutations of Omicron are presented in Figure  S1  in Supporting Information (SI). The AMBER19SB and GLYCAM06j force fields were used to describe proteins and glycans  26, 27. The systems were solvated in a rectangular box filled with 4-points OPC water molecules with a minimum distance of 1. 3 nm from the solute to the edge of the box  28. To neutralize the system, Na + and Cl -ions were added, maintaining the salt concentration at the physiological level of 0. 15 M. The GROMACS 2021. 3 package was used for MD simulation. The solvated systems were minimized by a steep descent algorithm for structure relaxation. The system was then equilibrated in NVT and then in NPT ensembles at 300 K and 1 atm for 500 ps and 5 ns MD runs, respectively.
MM-PBSA method In the MM-PBSA method, the binding free energy was obtained using the following equation: ΔGG bind = ΔGE elec + ΔGE vdW + ΔGG polar + ΔGG nonpolar -TΔSΔGS Here ΔGE elec and ΔGE vdW are the energies of the electrostatic and vdW interactions, and ΔGG polar is the polar solvation energy, which is calculated using the Delphi software  32. The non-polar solvate energy ΔGG nonpolar = γΔSASA, w SASA, where γ = 0. 0072 kcal/mol/nm 2 , and SASA is solvent accessible surface area calculated using gmx sasa tool in the GROMACS package with a solvent probe radius of 1. 4 Å  33. The entropy contribution TΔSΔGS was evaluated according to the method proposed by Duan et al  34.
Population of side-chain contacts formed by RBD residues with hACE2 at the interface. The results were obtained using conformations sampled over the last 100 ns of MD simulation. Notes:The authors declare no competing financial interest. Acknowledgements:This work was supported by Narodowe Centrum Nauki in Poland (Grant 2019/35/B/ST4/02086), the TASK Supercomputer Center in Gdansk, PLGrid Infrastructure, Poland, Department of Science and Technology, Ho Chi Minh city (Grant 13/2020/HĐ-QPTKHCN) and the HPCC at the Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam. Hoang Linh Nguyen was funded by Vingroup JSC and supported by the Master, PhD Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF. 2021. TS. 029.
65. The mains steps of the algorithm are: Selection of regions of interest-Contrast improvement-Image filtering using the Fourier transform-Binarization-Skeletonization-Correction of errors-Calculation of chosen parameters. The tool was implemented in MATLAB software. The contrast of the entry image is first improved by black and white inversion and histogram equalization to better separate the fringes from the background. The image is then converted into the frequency domain with a fast Fourier transform and filtered with a gaussian lowpass filter. The cutoff frequency was selected as 3. 333 nm -1 (0. 300 nm) -1 , meaning that objects separated by less than 0. 300 nm are attenuated. As the interlayer spacing in a graphenic structure is usually greater than 0. 3354 nm (d 002 of hexagonal graphite), no fringes information is lost.
A top-hat transformation is then applied to highlight high contrasted areas by correcting nonuniform illumination. The structural element for the top-hat transformation was a disk with an adjustable diameter larger than the apparent thickness of a single fringe to ensure the conservation of the fringes. The image is then binarized with a threshold determined using Otsu's method and skeletonized with MATLAB built-in skeletonization algorithm. Finally, a home-made algorithm is applied to correct Y or X fringe ends and aligned fringes separated by less than 0. 492 nm (two aromatic rings) are reconnected. The fringes shorter than 0. 492 nm are too short to have a physical meaning and are removed. The numerical tool measures the average crystallite size L a , the average fringes tortuosity (defined as the ratio of L a on the shortest distance between the fringe extremities), the average interlayer spacing d 002 and the number of graphene fringes stacked in a graphenic structure.
Acknowledgements The authors thank  Dr Nathalie Lyczko  for assistance with XRD,  Laurène Haurie  for her help with Raman spectroscopy and  Teresa Hungria  for the acquisition of the HRTEM images. The graphitization equipment used for this work is supported by the  French "Investissements d' Avenir" program  under the  Laboratory of Excellence ,  LABEX SOLSTICE ,  ANR-10-LABX-22-01  grant.
However, experience also shows that still many techniques which are self-evident to some scientists are inaccessible or unknown to others, even though these methods could often extensively aid their research. One class of objects which is ideal for the algorithmic "guess and prove" strategy turns out to be the class of holonomic sequences (to be defined below in §1. 1). This type of sequences is not only very common throughout mathematics and other sciences, but also provides a good algorithmic data structure and is very well studied from the theoretical point of view. Moreover, in Maple users can profit of an excellent package called gfun designed for manipulating and guessing holonomic sequences efficiently. Similar packages exist for other computer algebra systems like, for example, in Mathematica (e.
g. RATE, see  [Kra99] , or Guess by Kauers) or in SageMath (e. g. Guess in FriCAS by Rubey). The goal of this text is twofold. Our first aim is to give a short introduction to the practical use of Maple's package gfun, its various functions and the resulting possibilities. Secondly, we wish to explain the "art of algorithmic guessing" by means of two recent and very different results in mathematical research which were deduced with gfun's help. The ultimate target is to convince the reader that algorithmic guessing is very powerful and at the same time easy to do efficiently in Maple. The structure of the paper is as follows: in the Introduction ( §1) we explain the preliminaries and at the same time provide motivation for the objects of interest. We will describe very briefly the theoretical parts of the "guess and prove" technique in this context.
,   () together with the initial terms  0 ,. ,   , where  is the maximum between  and the largest integral root of   (), are enough to encode a given sequence. The general fact that linear differential equations form an excellent data structure from the computational point of view is propagated by All these closure properties are effective in the sense that there exist algorithms for performing them on the level of differential equations and recursions. As we will see, they are implemented efficiently in Maple's package gfun. We warn the reader that the quotient and composition of holonomic functions is not necessarily holonomic. For example the functions tan() and    -1 are not D-finite. Similarly, (1/  )  ≥1 , where   is the -th Fibonacci number is not P-recursive. From the theoretical point of view, linear differential equations have been studied by many outstanding mathematicians in the past two centuries.
Naturally, LCLM(, ) is defined as the least-order monic operator  ∈ Q()⟨⟩ such that  =  1  =  2  for some non-zero  1 ,  2 ∈ Q()⟨⟩, and  = GCRD(, ) is the monic operator of largest order such that  =  1  and  =  2  for some  1 ,  2 ∈ Q()⟨⟩. It can be proved that the solution spaces of  = 0 and  = 0 are vector spaces and that the LCLM produces an operator whose solution space is the sum of the spaces, while the solution space of GCRD(, ) is their intersection. Moreover, the LCLM and GCRD can be algorithmically computed using the "skew version" of the Euclidean algorithm; in practice, for example, with Maple's package DEtools. Then some elementary reasoning implies that the question of equality of two D-finite functions (and consequently two P-recursive sequences) is decidable and usually easy to answer in practice, see  [BLS17, §4.
Working with gfun Before we explain and show the most useful functions of gfun, let us mention a bit of history about this package and credit the developers. The Maple package gfun was written in 1992 by Salvy and Zimmermann. In the same year the authors submitted the article  [SZ94]  which was intended to be an introduction to the package and the reference manual at the same time. Since then gfun has been constantly improved by Salvy and got significantly better. Currently the newest version is 3. 84 and can be downloaded from his web page 3. The package also comes pre-installed with Maple, however with the version 3. 20 which is heavily outdated. One of the biggest improvements of the newest version compared to 3. 20 is the efficiency boosts briefly explained on the theoretical level at the end of the previous section.
Below we will indicate some more differences based on which we strongly recommend to download and use the newest version. Finally, we also mention the existence of the more recent Maple package NumGfun by  Mezzarobba [Mez10]  which deals with rigorous and efficient numerical computations with D-finite functions, since for some applications the two packages complement each other well. Almost all functions of gfun can roughly be divided into three categories: • Functions allowing interplay between the holonomic objects. • Effective closure properties for P-recursive sequences/D-finite functions. • Guessing algorithms for linear recurrences, ODEs and algebraic functions. We will briefly summarize the most useful functions and showcase them on some "toy examples". We note that this section is quite similar to the original technical report on gfun  [SZ94].
Now we translate both equations to differential operators using the Maple package DEtools. We can compute the LCLM  of the two operators, rewrite it as a differential equation and transform it back to a recurrence for the coefficients of the solutions: > L := LCLM(L_a, L_a_guess, [Dx,x]): > deq := diffop2de(L, y(x), [Dx,x]): > diffeqtorec(deq, y(x), u(n)): We find exactly the same recurrence relation as in equation (  5 ). Notice that the leading coefficient  3 () does not vanish for positive. Therefore, if the initial terms are prescribed to be ( 0 ,  1 ,  2 ), the differential equation corresponding to the operator  has the unique solution  ≥0. But since  is defined as the LCLM of the operators corresponding to the sequences (  )  ≥0 and (   )  ≥0 , it also annihilates  ≥0. This proves that   =   for all  ∈ N and consequently that our guessed recursion (6) is correct.
Minimal-order recursion. With the newest Maple version of 2021 we have a great shortcut thanks to van Hoeij's improvement in the package LREtools. We can namely directly algorithmically find the minimal-order linear recurrence after obtaining the one in §3. 1. 1 by just calling > LREtools['MinimalRecurrence'](rec_a,u(n)): We find exactly (6). This not only yields another proof of the correctness of the guessed (and then proven) recurrence, but also proves its minimality. Note that this method does not rely on guessing. 3. 1. 4 Guessing the ODE. Finally, we can also guess the differential equation for  ≥0     , prove its correctness and transform it to a recursion. This method has the advantage that we might discover a differential equation of smaller order than we would obtain by converting the recurrences above.
Since our solutions to (5) and (7) agree up to precision 3, they must be equal. Therefore the guess must be correct. shows that every solution of (  7 ) is a linear combination of Another solution which is completely different in spirit, but useful also for more general problems of deciding algebraicity, is to use the "guess and prove" method explained in §1. 2. We can first try to guess and then to prove minimal polynomials for  1 () and  2 (). This will not only provide a proof for algebraicity of the functions, but also give explicit minimal polynomials. In order to make the computations easier we will actually work with twelfth powers of  1 () and  2 (). Moreover, here we only explain the computations for  1 (), because the exact same code works for  2 () as well. 𝐴 1 (𝑥) 𝑢 1 (𝑥) • 2 𝐹 1 -1/ First we compute 100 terms of the series expansion for  1 () 12 : > f12 := hypergeom([-1/60, 11/60], [2/3], x)ˆ12: > ser1 := series(f12,x,100): Then we guess an annihilating polynomial for this series using gfun: > P := seriestoalgeq(ser1,y(x)): After a few seconds, this finds a polynomial (, ) ∈ Z[, ] of degree 20 in  and 4 in.
Acknowledgments: The author is deeply indebted to Alin Bostan who was not only a great source of motivation for this article, but is also a dedicated teacher and enthusiast of most techniques and ideas explained in it. Moreover, the author is also grateful to  Bruno Salvy  for the clarifications of several questions regarding the new version of gfun. Finally, we also wish to thank  Alin Bostan ,  Giancarlo Castellano  and the anonymous referees for careful reading of the manuscript and constructive comments. This work was financially supported by the  DOC  fellowship of the ÖAW (26101), the WTZ collaboration project of the  OeAD  ( FR 09/2021 ) and the  DeRerumNatura  project  ANR-19-CE40-0018.
By indicating the typelist variable as a third input to the gfun functions the user can force the algorithm to stick to one sequence type. We note that in the newest version of Maple 2021 great improvement on the package LREtools has been done by van Hoeij. One of the new available functions is GuessRecurrence which works essentially like listtorec. The art of algorithmic guessing in gfun 14421:9 finds (-4𝑛 -2)𝐶 𝑛 + (𝑛 + 2)𝐶 𝑛+1 = 0. We need at least 15 terms of the Almkvist-Zudilin sequence to find the correct recursion: > l := [1,-3,9,-3,-279,2997,-19431,65853,292329,-7202523, 69363009,-407637387,702049401,17222388453,-261933431751]: > listtorec(l, u(n)); finds (𝑛 + 2) 3 𝑢 𝑛+2 + (2𝑛 + 3)(7𝑛 2 + 21𝑛 + 17)𝑢 𝑛+1 + 81(𝑛 + 1) 3 > ser := series((1 -sqrt(1 -4*x))/(2*x),x,6);1 +  + 2 2 + 5 3 + 14 4 + 42 5 + ( 6 ) > seriestorec(ser, C(n)); Maple Trans.
Second, we have investigated the actual usage of these methods in the field. Specifically, we examined several hypotheses by conducting a systematic review of models published in the last ten years in JASSS: with or without a sample, such as Bayesian-based generation (Sun & Erath ), while classical algorithms, such as the iterative proportional fitting (IPF) procedure (see Subsection. ), do not need to be used in the generation process. Therefore, instead of the input data type, we set the distinguishing criterion as the synthesis technique to either create the properties of the entities or reproduce known real entities, termed as synthetic reconstruction (SR) and combinatorial optimization (CO), respectively. The first approach is based on the idea of synthetic reconstruction (Wilson & Pownall ) and consists of building populations through the random generation of individual characteristics.
Last step: Validation of the synthetic population. Validation is usually performed considering the distance metric between generated and input marginals for the attributes of synthetic entities, e. g. , distance between the distribution of age in synthetic population and input data regarding the distribution of age. In most cases, the quality of the synthetic population is assessed using the same dataset that has been used for the generation process. Hence, the validation of the synthetic population is performed out by measuring the distortion introduced by the generation process using the aforementioned distance metric. To this end, several indicators have been proposed.