dataesr/scientific-paragraphs-categorization huggingface dataset:
To illustrate this fact, we conducted a simple experiment in Fig. 1. Starting from two similar initial sampling trajectories, we let a multi-scale solver run for 14 epochs and 85 hours on the fastMRI knee database. We then evaluate the average reconstruction peak signalto-noise ratio (PSNR) on the validation set. As can be seen, the final point configuration and the average performance varies by 0. 3dB, which is significant. This suggests that the algorithm was trapped in a spurious local minimizer and illustrates the difficulty to globalize the convergence.
As discussed in the numerical experiments, the regularization effect allows optimizing the sampling density with a small dataset with a similar performance. Optimizing the function with as little as 32 reference images yields a near optimal density. This aspect might be critical for small databases. On the negative side, notice that we considerably constrained the family of achievable trajectories, thereby reducing the maximal achievable gain. We will show later that the trajectories obtained by minimizing (6) are indeed slightly less efficient than those obtained with (4). This price might be affordable if we compare it to the advantages of having a significantly faster and more robust solver requiring only a fraction of the data needed for solving (4).
In our setting, V models both the noise n and the input images x k. We consider V to be a random vector taken uniformly inside a database. In that setting, Bayesian optimization requires the following ingredients: 1. An initial sampling set. 2. A black-box evaluation routine of F (z, V ). 3. A family of interpolation functions together with a regression routine. We consider a total variation reconstructor and 25% undersampling. Similarly to the experiment in Fig. 4b , observe the numerous spurious minimizers occuring whatever the number K of images in the database. 4. A solver that minimizes the regression function. Hereafter, each choice made in this work is described. The initial sampling set To initialize the algorithm, we need the convex set C to be covered as uniformly as possible in order to achieve a good uniform approximation of the energy profile.
In this work, we used a maximin space covering design Pronzato (2017). The idea is to construct a discrete set Z = {z 1 ,. , z P } that solves approximately max Z∈C P min p ′ ̸ =p ∥x p -x p ′ ∥ 2. ( 12 ) In words, we want the minimal distance between pairs of points in Z to be as large as possible. This problem is known to be hard. In this work we used the recent solver proposed in  Debarnot and Weiss (2022)  together with the Faiss library  Johnson et al. (2019). The evaluation routine Evaluating the cost function (  6 ) is not an easy task. For just one realization of the noise n and image x k , we need a fast reconstruction method and a fast way to evaluate the non-uniform Fourier transform. The technical details are provided in the appendix A. Second, K might be very large. For instance, the fastMRI knee training database contains more than 30 000 slices of size 320 × 320.
The experimental setting Database and computing power Throughout this section, we used the fastMRI database  Zbontar et al. (2018). It contains MRI images of size 320 × 320. We focused on the single coil and fully sampled knee images. The training set is composed of 973 3D volumes, which represents a total of 34 742 slices. The validation set has 199 volumes and 7135 slices. Some images in the dataset have a significant amount of noise. This presents three significant drawbacks: i) the high-frequency contents of the images is increased artificially promoting sampling schemes making it possible to reconstruct noise, ii) the signal-to-noiseratio of the reconstructed images is decreased artificially and iii) we have shown that noise can dramatically impact the convergence of off-the-grid Fourier sampling optimization  Gossard et al.
Bayesian optimization: database size and numerical complexity In this section, we aim at evaluating the computational complexity of the Bayesian optimization routine. To this end, we study the impact of the number of images K in the dataset, the size of the initial sampling set and the number of iterations, which are governing the algorithm's complexity. Table  1  and 2 summarize our main findings for the total variation reconstruction and unrolled neural network. Table  1 : Bayesian optimization on a convex set C of dimension L = 20 using a total variation reconstruction algorithm and an unrolled network for 25% undersampling. The PSNR is evaluated for the optimized density on the validation dataset containing 7135 images. The total number of cost function evaluations is given in the second column.
In Table  1 , we see that the number of images K in the dataset has nearly no influence on the quality of the final sampling density. Taking K = 32 or K = 512 images yields an identical PSNR on the validation set. This holds both for the 25% and 10% undersampling rates. As can be seen in the Tables, reconstructing as little as 200 × 32 images is enough to reach the best possible density in the family. The same conclusion holds for the 10% undersampling rate. This represents 18% of a single epoch. We also see that the initial sampling set of the convex C plays a marginal role on the quality of the final result. In addition, taking a small number of initial points allows us to reduce the overall complexity of the algorithm to reach a given PSNR. Finally, Table  2  allows us to conclude that taking a database of 32 or 128 images has only a marginal influence on the computing times (3 hours instead of 4 hours) of the Bayesian optimization routine.
However, they correspond to slices which are not dominant in the dataset. On the other hand, the images that benefit the most from trajectory optimization correspond to central slices, prevalent in the set. As for the neural network, the best increases are obtained with the outer slices, which could be due to the large constant areas, the network is able to reproduce easily. Finally, the largest decreases for the neural network as a reconstruction mapping are not clearly associated to a specific type of slice. giving an optimized sampling scheme with guarantees on the underlying density with a reduced computational budget and with a reduced number of images. As can be seen, our approach requires only 32 images and 3 hours. This has to be compared to the 85 hours (3 days and a half) needed by the trajectory optimization routine.
Conclusion In this work, we designed efficient optimization algorithms that either optimize trajectories directly or learn a sampling density and an associated sampling pattern in MRI. Overall, the main highlights of this work are: The compressed sensing theories designed for the Fourier-Wavelet system with ℓ 1 reconstruction (e. g. Adcock and Hansen (2021) ) seem nearly optimal from an experimental point of view. Sampling schemes can be designed based on a density that is close to Shannon's rate at the k-space center and that decays towards the high frequencies. The precise shape of the density depends on the images structure. In that context, the Bayesian optimization of densities is an attractive method to design sampling schemes. It works with small datasets, ensures the convergence to a global minimizer.
(2019) , by changing the discrepancies and provided various improvements to the direct optimization of trajectories by using the Extra-Adam algorithm to handle hard constraints and by training reconstruction networks on families of operators. As a prospect, the extensions of these ideas to 3D multi-coil imaging is particularly relevant. There is no a priori obstacle to apply this rather lightweight formalism and to obtain dataset tailored sampling distributions. turned out to be inefficient in practice. We therefore resorted to an extension of Adam in the constrained case called  Extra-Adam Gidel et al. (2019). The step size was set to 10 -3 and the default Adam parameters β 1 = 0. 9 and β 2 = 0. 999. We observed no significant difference by tuning these last two parameters. We also use a step decay of 0.
A. 5. 2 Implementing the Non-uniform Fourier Transform (NUFT) Various fast implementations of the Non-uniform Fourier Transform (1) are now available  Keiner et al. (2009); Fessler and Sutton (2003) ;  Shih et al. (2021); Muckley et al. (2020). In this work, we need a pyTorch library capable of backward differentiation. Evaluating the gradient of the cost function in (4) or in (6) indeed requires computing the differential of the forward operator A(ξ) with respect to ξ. This can be done by computing D non-uniform Fourier transforms (see  Wang et al. (2022) ;  Gossard et al. (2022) ;  Wang and Fessler (2021) ). Different packages were tested and we finally opted for the cuFINUFFT implementation  Shih et al. (2021). The bindings for different kind of NUFT are available at https://github. com/albangossard/Bindings-NUFFT-pytorch/.
Figure5: Spurious minimizers with variations in the density space. Different sampling schemes are generated with the Sparkling algorithm for various target densities. The densities are linear combinations the two leading principal components, indexed by x and y in Fig. 5a. The sampling scheme corresponding to the density in the middle (x = y = 0) is displayed in Fig. 4a. The plots in Fig. 5bshow the energy profile for continuously varying target densities. The number of images K used to evaluated the energy varies from K = 1 (top) to K = 100 (bottom). The 3x3 densities in Fig. 5bare indicated by red crosses in Fig. 5b. We consider a total variation reconstructor and 25% undersampling. Similarly to the experiment in Fig. 4b, observe the numerous spurious minimizers occuring whatever the number K of images in the database.
Acknowledgments P. Weiss  and  F. de Gournay  were supported by the  ANR JCJC Optimization on Measures Spaces   ANR-17-CE23-0013-01  and the  ANR - P3IA-0004 Artificial and Natural Intelligence Toulouse Institute. This work was granted access to the  HPC resources of IDRIS  under the allocation AD011012210 made by  GENCI.
However, because of the severe underrepresentation of marine unicellular eukaryotes in modern sequencing databases, our understanding of the DNA methylation machinery in these organisms remains scarce. Diatoms are a dominant, abundant, and highly diverse group of unicellular brown microalgae (from 2 to 200 µm) of the stramenopile lineage. It is estimated that diatoms are responsible for nearly 20% of primary production on earth  29, 30. They are known to dominate marine polar areas and are major contributors of phytoplankton oceanic blooms. To date, 5mC has been reported only in four diatoms, Thalassiosira pseudonana  11  ,Cyclotella cryptica  31  , Fragilariopsis cylindrus  11  , and Phaeodactylum tricornutum  11, 27. Diatom methylation patterns strongly contrast with the patterns observed in animals but also dinoflagellates and plants  32.
Diatom genomes contain predicted proteins similar to members of the DNMT2, DNMT3, DNMT4, DNMT5, and DNMT6 family  11, 33. The conservation of their domain composition across eukaryotic groups as in the yeast Cryptococcus neoformans suggests that diatom DNMT5-like C5-MTases play a conserved and specific role in DNA methylation  11, 15. However, the functions of the DNMTs reported in diatoms have not been characterized in vivo. Recent advances in high throughput RNA sequencing technologies led to the development of the Microbial Eukaryote Transcriptome Sequencing Project (MMETSP)  34. The MMETSP concatenates more than 650 transcriptomes from diverse microeukaryote lineages, such as diatoms and dinoflagellates, making it the biggest sequence database for transcriptomes from individual marine microeukaryotes.
Here, utilizing the newly defined enhanced Domain Architecture Framework (eDAF) methodology  35  , we first explored the structural and phylogenetic diversity of DNMT sequences in marine microeukaryotes from the publicly available MMETSP sequencing databases. Using an integrative approach with available genomes and phylogenetic studies, we provide a DNMT phylogeny focused on the structural and domain diversity found in microeukaryote enzymes and discuss their evolutionary origins. We define, in the DNMT5 family, the sub-families DNMT5a, b and c enzymes, based on structure and phylogenetic assessment. The presence of the predicted DNMT5 family diversity remarkably contrasts with the apparent lack of DNMT1 in most of the MMETSP and microeukaryote databases. Using CRISPR/Cas9 genome editing, we present the functional characterization of the DNMT5a subfamily in the model diatom P.
Diversity of DNMT5 methyltransferases in microeukaryotes. To capture the diversity of 5-cytosine DNA methyltransferases encoded in microalgae, we applied a relaxed HMMER search (e = 1 as the cut-off threshold) for the PFAM DNMT (PF00145) domain on transcriptomes from the MMETSP database. The aim of this approach was to retrieve the maximum of DNMT hits between distantly related eukaryotes. In this study, we focused on DNMT1, DNMT3, DNMT4, DNMT5, and DNMT6 gene families that are known or represent putative DNA modifying enzymes. We retained sequences showing conserved DNMT domains and depicted their domain structures using eDAF analysis  35. We built a representative phylogeny of DNA methyltransferases based on the alignment of conserved DNMT motifs (Fig. 1a , Supplementary Fig. 1 , Supplementary Data 1).
Since DNMT2 is an aspartic acid transfer RNA methyltransferase  25  , published microalgal DNMT2 sequences were used as additional sequences for phylogenetic analysis. The tree construction exploited the stability of Bayesian approaches to deal with the fast evolution rates observed in our DNMT sequences. Methods based on posterior probabilities present more support values than random sampling algorithms when facing high mutation rates  [37] [38] [39]. The MMETSP database is composed of transcripts and is thus deprived from lowly expressed genes or pseudogenes. The relative absence of a given gene family within a species will therefore be interpreted accordingly. We found three gene families related to the DNMT5 clade of enzymes that we named DNMT5a, DNMT5b, and DNMT5c (Fig. 1a ). The sequence alignments show homology in the functional DNMT motifs (I-IV, VII, and X) that contain the S-Adenosyl methionine binding and catalytic domains within DNMT5s (i.
51). Of note, DNMT5a is found in distantly related eukaryote lineages. We found 76 species with at least one DNMT5 orthologue. We found a DNMT5a in the green algae Tetraselmis astigmata but also in haptophytes and the marine photosynthetic excavate euglenozoa Eutreptiella gymnastica. The DNMT5a family is also found in stramenopiles, including diatoms, bolidomonas, pelagophytes, and dictiochophytes, as well as in fungi (former Cryptococcus DNMT5-related enzymes) (Fig. 1a , Supplementary Data 2). The DNMT5b enzyme is found in diatoms, Bolidomonas pacifica and haptophytes. Emiliania huxleyi DNMT5 enzymes are not found in other haptophytes in the MMETSP database. In addition, the phylogenetic position of E. huxleyi DNMT5 proteins are not very supportive. First, E. huxleyi DNMT5a protein is not monophyletic with other ochrophyte DNMT5s and its DNMT5b appears as an outgroup found in diatoms.
We first confirmed that orthologues of T. pseudonana DNMT4 enzymes are widespread in diatom transcriptomes and genomes. A total of 8 pennate and 23 centric diatoms out of 60 diatom species, express or encode at least one DNMT4 related transcript (Supplementary Data 3). This finding suggests that the family is ancestral in diatoms. In our analysis, no DNMT4 enzymes were found in other species of the MMETSP database. Phylogenetic analysis indicates that RID and diatom DNMT4s may form a moderately supported monophyletic family of enzymes (Fig. 1a ). At the structural level, both RID and diatom DNMT4 enzymes diverged compared to DNMT1 enzymes, and also between each other. Most diatom DNMT4 enzymes are composed of a single DNMT domain as in T. pseudonana, which also contrasts with fungal enzymes (Fig.
1b , Supplementary Data 4). Nonetheless, nine diatom DNMT4 proteins possess an additional N-terminal chromodomain as observed in Thalassiosira miniscula (Fig. 1b , Supplementary Data 3 and 4). Furthermore, we found two putative DNMT1-like enzymes in the transcriptomic database of two Raphidophyceae brown microalgae: Heterosigma akashiwo and Chatonella subsalsa. They are composed of a conserved DNMT domain and a plant homeodomain (Fig. 1b , Supplementary Fig. 1 , Supplementary Data 4) but poorly defined a monophyletic gene family with either DNMT1s or DNMT4s. Interestingly, we found a DNMT1-related enzyme in three haptophyte species out of four (Gephyrocapsa oceanica, Isochrysis. sp-CCMP1324 and Coccolithus pelagicus) from the MMETSP database that cluster with annotated CMTs found in the coccolithophore E.
4b, 5 ), consistent with the putative role of DNMT5 in maintaining DNA methylation patterns in diatoms. To generate a quantitative single base resolution of DNA methylation loss in DNMT5:KOs, we performed whole genome bisulfite sequencing in M23, M25 (considered as two biological replicates) and the reference, Pt1 8. 6 line. We filtered cytosines by coverage depth considering a 5X coverage in all cell lines as a threshold and computed CG methylation levels in TEs and genes. We found that CG methylation is severely impaired in M23 and M25 compared to Pt1 8. 6 cell line (Fig. 3a, b , Supplementary Data 6). This is particularly observed within TEs that are the targets of DNA methylation in P. tricornutum (Fig. 3a, b ). To get a quantitative view of the loss of DNA methylation in DNMT5:KOs, we defined differentially methylated regions (DMRs).
5e , Supplementary Data 17). This suggests that younger TEs tend to be direct targets of DNA methylation compared to evolutionary older TEs family members. Subsequently, loss of DNA methylation causes upregulation of mainly younger TEs. Filloramo et al. 47  recently described 85 long-LTR-copia-like (LTR-copia) TEs based on reannotation of the P. tricornutum genome by Oxford Nanopore Technologies long-read sequencing. Such TEs are considered as potentially still active  47. They are represented by Copia-like in diatoms (CoDi) of the CoDi5, CoDi4 and CoDi2 families  47  that corresponds to the TE families found overexpressed in our datasets (Fig. 5d ). Accordingly, we found that 75/85 of LTR-copia are targets of DNA methylation and are associated with common hypoDMRs (Supplementary Data 18).
Discussion Studies on the evolutionary history of DNMTs have established that the DNA methylation machinery diverged among eukaryotes along with their respective DNA methylation patterns  2, 11. However, the diversity of DNMTs found in SAR lineages is underexplored due to the lack of representative sequences. Based on MMETSP transcriptomes, we set out to explore the diversity and phylogeny of DNMTs in early diverging eukaryotes. Besides the absence of genomic sequences, the MMETSP database only encompasses expressed transcripts from cultured organisms and is thus deprived of lowly expressed genes and condition-specific expressed genes. Absence of a given gene family within a species should therefore be interpreted accordingly. When our analysis found multiple distinct transcripts sharing the same DNMT subfamily, as in diatoms, we used the most probable open reading frame translation of the transcripts using eDAF curation to produce our phylogenetic tree.
Methods HMMER and Reciprocal BLAST best Hit analysis. We performed an extensive scan of the MMETSP database, enriched with 7 diatom transcriptomes and genomes from the top 20 most abundant diatoms found in Tara Oceans database  62  , using HMMER-search with the model PF00145 to fetch any DNMT-like, including partial transcripts, sequence within microeukaryotes. We ran HMMER in a nonstringent fashion to not miss positives DNMT sequences. We used eDAF approach to filter the expected high number of false positives. It is worth noting that we initially use HMMER for screening instead of the built-in module of eDAF due to the time complexity of the latter for extensive searches (tens to hundreds of times slower than HMMER). Reciprocal BLAST best hit analysis was performed as previously described  63.
Briefly, the DNMT3 (Phatr3_J47136), DNMT4 (Thaps3_11011), DNMT5 (Phatr3_EG02369) and DNMT6 (Phatr3_J47357) orthologues found in P. tricornutum or T. pseudonana (for DNMT4) were blasted against a phylogenetically optimized database that include MMETSP transcriptomes. Putative DNMT sequence hits giving back the corresponding enzyme (DNMT3, DNMT4, DNMT5, or DNMT6) at the threshold of e-value of 1 × 10 -5 in the corresponding diatom were retained. Candidate enzymes were then analyzed using eDAF. eDAF-guided domain architecture analysis. enhanced Domain Architecture Framework (eDAF) is a four-module computational tool for gene prediction, gene ontology, and functional domain predictions  35. As previously described for Polycomb and Trithorax enzymes  35  , candidate DNMTs identified by RBH and HMMER-search were analyzed using the DAMA-CLADE guided built-in functional domain architecture to predict the occurrences of DNMT domains starting from protein sequences.
The domain architecture of representative enzymes used in this study can be found in Supplementary Data 4. Phylogenetic tree analysis. The DNMT domain of candidate enzymes were aligned using ClustalΩ  64  (HHalign algorithm). The alignment was manually curated and trimmed using trimAL (removing >25% gap column) to align corresponding DNMT motifs in all gene families. A convergent phylogenetic tree was then generated using the online CIPRES Science gateway program  65  using MrBAYES built-in algorithm. Default parameters were used with the following specifications for calculation of the posterior probability of partition: sumt. burninfraction = 0. 5, sump. burningfraction = 0. 5, 10000000 generations, sampling each 100. We also used two different models: Estimating the Fixed Rate and GTR. Cell cultures.
In addition, all mutants show loss of heterozygosity (LOH). RNA and DNA extraction. Total RNA extraction was performed by classical TRIZOL/Chloroform isolations and precipitation by isopropanol. Frozen cell pellets were extracted at a time in a series of 3 technical extraction/duplicates and pooled. RNA was DNAse treated using DNAse I (ThermoFisher) as per manufacturer's instructions. DNA extraction was performed using the Invitrogen™ Easy-DNA™ gDNA Purification Kit following 'Protocol #3' instructions provided by the manufacturer. Extracted nucleic acids were measured using QUBIT fluorometer and NANODROP spectrometer. RNA and gDNA Integrity were controlled by electrophoresis on 1% agarose gels. RT-qPCR analysis. qPCR primers were designed using the online PRIMER3 program v0. 4. 0 defining 110-150 amplicon size and annealing temperature between 58 °C and 62 °C.
Primers used in this study are listed in Supplementary Data 19. Dot blot. gDNA samples were boiled at 95 °C for 10 min for denaturation. Samples were immediately placed on ice for 5 min, and 250-500 ng were loaded on regular nitrocellulose membranes. DNA was then autocrosslinked in a UVC 500 crosslinker -2 times at 1200uj (*100). The membranes were blocked for 1 h in 5% PBST-BSA. Membranes were probed for 1 h at room temperature or overnight at 4 °C with 1:1000 dilution of 5mC antibody (OptimAbtm Anti-5-Methylcytosine -BY-MECY 100). 5mC signals were revealed using 1:5000 dilution of HRP conjugated antirabbit IgG secondary antibody for 1 h at room temperature followed by chemo luminescence. Loading was measured using methylene blue staining. RNA and bisulfite sequencing. RNA libraries were prepared by the FASTERIS Company (https://www.
Acknowledgements We thank  Catherine Cantrel  form  IBENS  for media preparation. L. T. acknowledges funds from the  CNRS , the region  of Pays de la Loire  ( ConnecTalent EPIALG project)  and  Epicycle ANR project  ( ANR-19-CE20-0028-02 ). C. B. acknowledges funding from the  ERC Advanced Awards Diatomite. F. Y. was supported by a  PhD fellowship  from the  Chinese Scholarship Council  ( CSC-201906310152 ).