dataesr/scientific-paragraphs-categorization huggingface dataset:
This topology is replicated in three instances, one per leaf tissue, and leaf identity is used as a covariate in the model so that leaf-specific parameter values are estimated. This approach assumes that no exchange of nitrogen across proteins or across leaves occurs once nitrogen is incorporated into a protein. Finally, we assume that the N content in the medium is so large that it is constant compared to the protein pools, so we set it to a steady state in the model (Figure  4a ). This is equivalent to the zero-order process assumed by  Li et al. (2017)  for protein synthesis. From a modelling perspective, the dataset from  Li et al. (2017)  contains all the data needed for an analysis with isotracer: a time series for compartments enrichment (labelled fractions) and a time series for compartment sizes (relative protein abundances).
| Nitrogen cycle in a Trinidadian mountain stream Tracer addition experiments have been used profitably in ecology to identify the strength of trophic connections and to quantify nutrient cycling in ecosystems. In a study by  Collins et al. (2016) , the authors quantified the nitrogen exchanges in the food webs of mountain streams in Trinidad, from the dissolved nutrients (NH + 4 and NO - 3 ) to the invertebrate consumers. They examined the effect of light conditions and of the presence/absence of a fish consumer on the nitrogen dynamics in the food web. Data were collected by dripping 15 N-enriched ammonium into two streams in Trinidad, and samples from each food web compartment were taken during the drip and after the drip in several transects in each stream. The transects were located at different locations downstream of each drip.
The drip phase lasted 10 days, and the post-drip phase lasted 30 days (Figure  3 ). Compartment enrichment was measured by determining 15 N/ 14 N ratios by mass spectrometry, while compartment sizes were estimated in mgN/m 2 using various field sampling techniques depending on the compartment type (dissolved, primary producer, invertebrate). Streams differed in their exposure to sunlight (natural vs. trimmed canopy) and transects within streams differed in the presence/absence of guppies (Poecilia reticulata). The dataset used in  Collins et al. (2016)  is shipped with isotracer as the lalaja table. In this case study, we will use the data from only one stream and a subset of the original food web for simplicity, but a full analysis including both streams and using the framework used in isotracer was presented in  López-Sepulcre et al.
We used data from three transects from one stream (Upper LaLaja, for which the canopy cover was thinned). The transects differed in their effective addition regime due to their different distances from the drip source, but otherwise were used as simple replicates in our model (i. e. they shared the same parameter values). We used DIC to compare the models: the ΔDIC between the models was relatively small (2. 66), and suggested that the model without the candidate trophic F I G U R E 5 Modelling of phosphate absorption in Zostera marina tissues under dark and light conditions using data from  McRoy and Barsdate (1970). (a) Sankey plot summarizing estimated average phosphate flows between study system compartments. The width of the connectors is proportional to the estimated flows. In the original experiment, upper and lower water compartments are separated by a septum.
| CURRENT LIMITATIONS , E X TEN S IB ILIT Y AND FUTURE D IREC TI ON S The isotracer package implements a Bayesian approach to model tracer addition experiments and to estimate parameter uncertainty. Its primary aim is to allow researchers whose typical expertise might not cover statistical modelling of systems governed by ordinary differential equations to perform rigorous and reliable statistical analyses, so that the valuable data produced by tracer addition experiments can be fully taken advantage of. The package is built upon the versatile probabilistic programming language Stan, but provides a user-friendly interface to define network structure and experimental design that does not require the user to write any Stan code and makes quick prototyping of models possible. isotracer allows for modelling of a variety of addition designs (pulse, drip, pulse-chase), can take into account both stable and decaying (e.
Such first-order reactions result in simple systems of differential equations, and offer in most cases a good approximation to the modelled network dynamics on the timescale of the experiment. However, in some scenarios, second-order reactions, or more complex equations, govern the material flows. In other cases, the rate coefficients are not constant over the timescale of the experiment (e. g. time-dependent rate of glucose uptake from bloodstream after injection). The isotracer package can be extended with more complex models to be able to model such cases, including cases where several sources must react together following stoichiometric constraints (e. g. kinetic flux profiling of known metabolic pathways;  Yuan et al. , 2006). Such a task would involve extending both the Stan code (to calculate the expected compartment trajectories in the Stan model) and the R code (to provide the interface to those new models and to define the post-run methods used, for example, to perform posterior predictive checks on the Stan output).
ACK N OWLED G EM ENTS We thank  Sarah Collins ,  Sebastiano De Bona ,  Rana El-Sabaawi ,  Swanne Gordon ,  Sophia Lambert ,  Alex Lee  and  Steven Thomas  for discussions. Sarah Collins  and  Jonathan Benstead  helped test the package interface. We are also grateful to an anonymous reviewer and to  Prof. Bob Hall  for their thorough and constructive feedback on the submitted manuscript. Funding was provided by the  Academy of Finland  (grant number  295941 ).
SOM: Self-Organizing Maps The classical Self-Organising Maps (SOM) initially proposed by Kohonen  [2]  consists of an ensemble of neurons, each associated with a weight vector, organized in a lowdimensional lattice (Usually from one to three dimensions) and with defined update rules enabling unsupervised quantization of arbitrary dimension input vectors. During the learning phase, the vectors of the input set are successively presented to every neuron of the network. At each new input, the neuron with the closest weight vector to the input vector (according to a distance function) is elected as the winning neuron and called the Best Matching Unit (BMU). Weights of all the surrounding neurons are then updated toward the new input, with decreasing influence, starting from the BMU. This process repeated over the training dataset enables the neurons to learn by mapping the input vector space in a self-organizing manner.
ACSOM embodiment will enable real-time weight updates driven by physical input data. We have ongoing work on building extension boards permitting to endow SCALP with sensors (cameras, microphones, touch). Such multiplicity of input data from different sensors will permit us to apply ACSOM to multi-modal learning that could be of particular interest for tracking with incomplete or faulty input data. Performance improvement will be addressed by parallelising and pipelining the processing of multiple input vectors. Several nodes will serve as data inputs (i. e. different sensors connected to different boards), different data input broadcast will be performed simultaneously in an asynchronous manner. The use in parallel of the ACSOM nodes processing pipelines will permit to handle a multiplicity of states for the ongoing learning iterations.
1b ). In Phase 1, we performed amplicon sequencing (AmpliSeq, ~1000 X) profiling the entire open reading frame of 87 genes previously detected in FCD/HMEs or known PI3K-AKT3-mTOR interactors ('MCD panel v1', Supplementary Table  2a ). In Phase 2, for 75 unsolved cases from Phase 1 and additionally collected 54 cases, we performed unbiased deep whole-exome sequencing (WES, ~300 X) on paired samples, where available, or on unpaired samples (i. e. brain plus blood/saliva vs. brain only). In Phase 3, from an additional subcohort of 132 new cases, we designed the 'MCD panel v2' (Supplementary Table  2b ) including known and novel genes detected in Phases 1 and 2 (Extended Data Fig. 1 , Methods). We re-sequenced unsolved cases from Phase 2, expecting that the higher read depth afforded by panel sequencing could provide greater sensitivity to detect low VAF mutations, and used BSMN best practice guidelines for mapping and variant calling  12.
MCD genes enriched in the excitatory neuronal lineage To infer the cell type in which MCD genes function, we accessed a published single-cell transcriptome dataset from the 2nd-trimester human telencephalon, at a time when these mutations probably arose  41  (Fig. 5a ). We generated an eigengene, by mapping the average expression of our MCD genes against the UMAP plot (Fig. 5b ). This showed a strong positive correlation with dividing radial glial cells, and a moderate correlation in dividing intermediate progenitor cells (IPCs) and mature excitatory neuron cells. We found a negative correlation with inhibitory neuronal lineages including medial and central ganglionic eminences (MGE, CGE) and mature interneuron clusters (Fig. 5c ). We next performed deconvolution into four major module eigengene (MEs), which revealed cell types classified as mature excitatory neurons (turquoise and blue), microglia (brown), and unassigned (grey) (Fig.
Next, we investigated the expression patterns of MCD genes in this HME/TSC snRNAseq dataset. An eigengene representing expression patterns of MCD genes was enriched in Ast-L1/3 and OD-L, which were labeled as dysplastic cells (Fig. 6c ). Interestingly, the individual MCD genes displayed converging expression patterns resulting in six different eigengenes (Fig. 6d , gene members for each eigengene are described in Extended Data Fig. 7 ) which show distinct enrichment patterns across cell types (Fig. 6e ), implying that membership of each eigengene may be associated with the pathophysiology of the corresponding dysplastic cell type in HMEs. We performed a pseudo-bulk DEG analysis comparing HME with CTRL and detected 590 up-regulated genes and 1096 down-regulated genes. Intriguingly, 20% (15/75) of MCD mutated genes in our list overlapped with DEGs of HME.
Orthogonal validation and quantification of mosaic mutations with targeted amplicon sequencing Targeted amplicon sequencing (TASeq) with Illumina TruSeq was performed with a coverage goal of >1000X for 554 candidate variants detected by computational pipelines described above for both MPAS and WES, to experimentally validate the mosaic candidates before functional assessment. PCR products for sequencing were designed with a target length of 160-190 bp with primers being at least 60 bp away from the base of interest. Primers were designed using the command-line tool of Primer3  50, 51  with a Python (v3. 7. 3) wrapper  13, 14. PCR was performed according to standard procedures using GoTaq Colorless Master Mix (Promega, M7832) on sperm, blood, and an unrelated control. Amplicons were enzymatically cleaned with ExoI (NEB, M0293S) and SAP (NEB, M0371S) treatment.
Single-nucleus RNAseq bioinformatics pipeline Fastq files from single-nucleus libraries were processed through Cell Ranger (v6. 0. 2) analysis pipeline with -include-introns option and hg19 reference genome. Pooled library was demultiplexed and singlets were taken by demuxlet. Seurat (v4) package was used to handle single nuclei data objects. Protein coding genes were used for further downstream analysis. Nuclei passed a control filter (number of genes > 500, number of reads >1000, percentage of mitochondrial gene < 10%) was used for downstream analysis. Data were normalized and scaled with the most variable 5000 features using the 'NormalizeData' and 'ScaleData' functions. Dimensionality reduction by PCA and UMAP embedding was performed using runPCA and runUMAP function. Clustering was performed by FindNeighbors and FindClusters function.
Weighted gene co-expression network analysis 'r-wgcna' package (v1. 69) was used for WGCNA according to instructions (PMID: 19114008). Briefly, a similarity matrix was generated based on Pearson's correlation coefficient value among the top 3000 variable features in single-nucleus transcriptome data, which was used to calculate the subsequently signed type of network adjacency matrix. Next, the topological overlap matrix (TOM) and the corresponding dissimilarity (1-TOM) value were generated from the adjacency matrix. Finally gene modules were generated by 'cutreeDynamic' function with 'tree' method, minAbsSplitHeight = 0. 9 and minClusterSize = 30 option. Similar gene modules were merged by 'mergeCloseModules' function with cutHeight = 0. 25. String analysis was performed using each gene module for the identification of the given module's functional characteristics.
A subset of the somatic mutations was further functionally validated by mouse modeling. Candidate genes were annotated and correlated with external datasets such as STRING DB, clinical phenotype dataset, and newly generated single-nucleus RNAseq dataset from MCD brain. (c) Somatic variant calls were detected from all three phases of genetic discovery, yielding 108 validated somatic calls. (d) Correlation between square-root transformed (sqrt) AmpliSeq/WES variant allele fraction (VAF) and TASeq VAF. Solid line: best-fit line linear regression. Dotted lines: 95 % confidence band of the best-fit line. (e) Oncoplot with all 69 validated somatic SNVs from this study. Top: most patients had one gene mutated, a few patients had more than one gene mutated, and patient HME-4144 had 11 different validated gene mutations.
The validation of the snRNAseq result from HME-6593 shows MCD dominant clusters are highly correlated with dysplastic cells in MCD. (a) H&E staining (left) and RNAscope (right) staining results in several MCD-dominant markers (FGFR2, FGFR1, EGFR) in the same formaldehyde-embedded-paraffin-fixed section. (b) H&E and RNAscope result in another section with different RNA probes (FGFR3 and PDGFRA) enriched in MCD clusters. Dashed lines indicate blood vessels. White/black arrows are pointing to the dysplastic cells. Extended Data Fig. 7 Expression patterns of individual MCD genes in the MCD snRNAseq dataset. The gene members of each eigen module shown in Fig. 6d were colored according to the name of a given eigengene.
Acknowledgments AmpliSeq, TASeq, and snRNAseq were supported by  NIH   P30CA023100  and  S10OD026929  at the  UCSD IGM Genomics Center. Rady Children's Institute for Genomic Medicine, Broad Institute  ( U54HG003067 ,  UM1HG008900 ), the  Yale Center for Mendelian Disorders  ( U54HG006504 ), and the  New York Genome Center  provided whole-exome sequencing. UCSD Microscopy core ( NINDS P30NS047101 ) provided imaging support. CC was supported by a 2021  Brain & Behavior Research Foundation   Young Investigator Grant. This study was supported by the  NIH  ( NIMH U01MH108898  and  R01MH124890  to JGG and GWM, and  NIA R21AG070462 ,  NINDS R01NS083823  to JGG). We thank  Sté phanie Baulac  and  Sara Baldassari  for sharing unpublished exome data.
Code and data availability Code to generate the figures and analyze the data are publically available on GitHub (https://github. com/shishenyxx/MCD_mosaic). WES and AmpliSeq data are deployed on NIMH Data Archive under study number 1484 "Comprehensive multiomic profiling of somatic mutations in malformations of cortical development" and SRA under accession number PRJNA821916: "Comprehensive multiomic profiling of somatic mutations in malformations of cortical development". The snRNAseq R object was deposited in Single Cell Portal (https://singlecell. broadinstitute. org/single_cell/study/SCP1815/comprehensive-multiomicprofiling-of-somatic-mutations-in-malformations-of-cortical-development#study-download).
Extended Data Fig. 6 6 The validation of the snRNAseq result from HME-6593 shows MCD dominant clusters are highly correlated with dysplastic cells in MCD. (a) H&E staining (left) and RNAscope (right) staining results in several MCD-dominant markers (FGFR2, FGFR1, EGFR) in the same formaldehyde-embedded-paraffin-fixed section. (b) H&E and RNAscope result in another section with different RNA probes (FGFR3 and PDGFRA) enriched in MCD clusters. Dashed lines indicate blood vessels. White/black arrows are pointing to the dysplastic cells. Extended Data Fig. 7 Expression patterns of individual MCD genes in the MCD snRNAseq dataset. The gene members of each eigen module shown in Fig. 6d were colored according to the name of a given eigengene.
This idea is supported by the fact that in many applications, queried k-mers come from partially assembled reads or succinct representations, such as SPSS  [7, 8] , or Colored de Bruijn graphs  [9] , that is, only k-mers present in the original data are queried for their frequencies. The idea of storing only counter information and not k-mers is also supported by the observation that the number of distinct k-mer counts in genomic data is relatively small. It is known that k-mer counts in genomes obey a "heavy-tail" power-law distribution 1 with a relatively large absolute value of the exponent  [10, 11]. For such distributions, the number of distinct k-mers makes a linear fraction of the data size, while the number of distinct k-mer counts is relatively 1 Here we assume k to be sufficiently large, typically k > log 4 L, where L is the data size.
A PREPRINT -NOVEMBER 13, 2020 small. For example, for the human genome and k = 27, there are about 2. 5 billions distinct k-mers but only about 8,000 distinct frequency values. This is because the majority of k-mers have a very small count: in the above example, 97% of k-mers are unique and 99% of k-mers have a count of at most 5. Frequent k-mers often tend to have an identical count as well, due to transposable elements: for example, k-mers specific to Alu repeats in primate genomes will likely have the same count. Our contribution. We propose a new probabilistic data structure that we call Set-Min sketch capable to represent k-mer count information in small space and with small errors. The sketch guarantees that the expected cumulative error obtained when querying all k-mers of the dataset can be bounded by εN where N is the number of all k-mers (i.
e. essentially, the size of the dataset). We provide a theoretical analysis in order to dimension the sketch according to the desired error bound. We further present experimental results on a range of datasets illustrating the benefits of our approach, and compare it with alternative solutions: Count-Min sketch and Minimal Perfect Hashing. Note, finally, that Set-Min sketch is a general data structure in that it can be used to efficiently represent a mapping of k-mers to any type of labels, provided that the number of possible labels is relatively small. Applications. Set-Min sketch can have different use cases. In this paper, we explore the probabilistic compression of genomic k-mer counter tables in case of large k values. Thanks to the characteristic skewed distribution of the frequencies for large ks, a Set-Min sketch is able to provide a more space-efficient map than other representations with low errors.
One application of Set-Min sketches, not explored here, is to act as a temporary representation while building more complex structures based on counters. Consider, for example, the exact computation of weighted pairwise distances between all pairs of genomes in a given set. Examples of such distances are the Bray-Curtis similarity measure, see e. g. [12] , or Weighted Jaccard similarity estimation  [13]. The most naive algorithm is to first produce count tables for each dataset and then compare them pair-wisely to produce the desired output. Instead of storing whole tables, one can store multiple Set-Min sketches together with a presence-absence data structure, such as a Bloom filter. By doing so, the weighted comparison computation is reduced to a single pass through the presence-absence data structure with the counters of a given k-mer retrieved on-demand from the Set-Min sketches of the datasets in which the k-mer is found.
In this work we assume that only k-mers present in the dataset can be queried. In this case, a query can no longer result in an empty intersection. We further optimize by not storing in the sketch the label 1 with the largest support. For large k, 1 is usually 1, which is the frequency of the largest fraction of k-mers. 1 is retrieved implicitly: when the intersection is empty, 1 is returned. This optimization allows us to save space and will be further discussed later. Note that, with these modification, an error may occur even if the resulting intersection is a singleton but the right label is actually 1 and not the label obtained.
Bounding the total error We now show that with Set-Min sketch, we can bound the total absolute error over all k-mers present in a dataset. Consider a sketch S built on a map assigning to each k-mer p ∈ K a value (label) p ∈ L which is the frequency of p in the dataset. We denote by c the number of k-mers with frequency ∈ L (spectrum value). Consider D = p∈K | ˆ p -p | (1) where p is the label of p returned by the sketch. Our goal is to dimension R and B such that D ≤ ε a 1 , where a 1 is the total number of k-mers in the dataset (roughly, the dataset size) and 0 < ≤ 1. Querying p returns an incorrect frequency m = p iff m occurs in the intersection and c m < c p. The probability of this event is 1 -1 - 1 B cm R ≈ 1 -e -cm B R (2) 4 and the expectation of the error when querying p is then cm<c p m∈L |m -p | 1 -e -cm B R.
Implementation We implemented Set-Min in a software tool named fress, available at https://github. com/yhhshb/fress. The fress pipeline compares Set-Min with Count-Min and MPHF implementations. BBHash  [19]  (https://github. com/ rizkg/BBHash) is the only external library required for comparison as Count-Min is implemented within fress. Rather than storing a set in each bucket of the sketch, fress only stores an index to an array of involved sets. Note that its purpose is to only validate the approach, and it does not include any complex optimisation, such as multi-threading or bit-packing of the final matrix. Sorted spectra and lists of involved sets are explicitly stored in text format in order to be human-readable and allow for an easier analysis of the results.
Set-Min vs Count-Min sketch For ease of comparison, column T reports the threshold ε a 1 given to Algorithm 1. Columns E s and E c report the actual total sum of errors for Set-Min and Count-Min, respectively. In all reported cases E s < T , as expected. The total error of Count-Min, E c is, most of the time, one order of magnitude larger than E s. For SRR622461 with k = 15, it even exceeds the total number of k-mers a 1 in the dataset. The average error of Set-Min is, in most cases, very close to 1, which suggests that the overwhelming majority of collisions occur between successive counts. Most of them occur between counts 1 and 2, the most abundant ones in the spectra considered here. The average error of Count-Min is bigger but of the same order of magnitude, except for small k and unassembled datasets.
Presence-absence information As introduced in Section 3. 2, in this work we assumed that only k-mers present in the dataset can be queried. This assumption allowed us to discard the largest value of the spectrum corresponding to unique k-mers, thereby saving more space than a complete sketch. Set-Min sketches can seamlessly work without this assumption, but the space required for storing k-mer counters may not be competitive to other solutions. An alternative is to build an additional data structure, specifically optimized to answer presence/absence queries (such as a Bloom filter), as a complement to Set-Min sketches. Another scenario occurs when working with multiple datasets of very high similarity, such as a large collection of bacterial strains or a collection of RNA-seq data  [22, 23].