dataesr/scientific-paragraphs-categorization huggingface dataset:
SOTIP recovers known differential microenvironments in cirrhotic liver The last task of SOTIP is differential microenvironment analysis (DMA), which aims to identify microenvironments between conditions (e. g. disease status, drug treatment, and experimental perturbation) with high specificity. This task is in analogy with the differential abundance analysis task  [54] [55] [56]  in single cell analysis, but unavailable in spatial omics analysis. To demonstrate the utility of SOTIP on this task, and as a sanity check, we firstly applied DMA in a spatial metabolomics dataset including two samples from healthy and fibrotic liver (Fig. 6a  for illustration). They provided paired H&E staining, which could be taken as a positive control for our detection result (Fig. 6b ). The healthy liver sample (Fig.
SOTIP identifies highly specific MECNs associated with prognosis in subtypes of TNBC Triple-negative breast cancer (TNBC), defined by lack of therapeutic targets (estrogen receptor, progesterone receptor, and Her2), is considered to be a form of breast cancer with more aggression and poorer prognosis  82. Keren et al. 12  applied multiplexed ion beam imaging by time-of-flight (MIBI-TOF) to generate a 36-plex spatial single cell proteomics dataset from 41 TNBC patients. In that paper, the researchers classified TNBC patients into three archetypical subtypes (viz. , cold, mixed, and compartmentalized), by quantifying the mixture degree of tumor and immune cells  12. The dataset hasn't been fully mined since the original paper mainly concentrated their analysis on protein co-expression and basic spatial statistics  12  , we here focused on the microenvironment to draw a spatial organization of the tumor- immune landscape and to inspect interesting microenvironment with strong specificity.
We also performed exhaustive comparisons between SOTIP and state-ofart methods on different spatially resolved datasets. In the task of SHN quantification, we benchmarked SOTIP against NUCC and IGD by delineating the nuclear envelope in HeLa cell line (spatial proteomics, 4i  23  ) and recovering the gradient heterogeneity pattern in mouse brain cortex (spatial transcriptomics, osmFISH  46  ). In the task of SDM identification, we firstly showed SOTIP's superior performance compared with other spatial clustering algorithms on the commonly used Spa-tialLIBD dataset of human brain cortex  48  (spatial transcriptomics, 10x Visium). On another spatial transcriptomics dataset of mouse brain cortex  46  , SOTIP also outperformed others in terms of ARI. We validated the compatibility of SOTIP on other spatial omics data by collecting samples from CRC (spatial proteomics, scMEP  49  ) and TNBC (spatial proteomics, MIBI  12  ).
Although SpaGCN is also extendable to spatial proteomics dataset, SOTIP showed better performance when comparing with the ground truth in multiple cases (Fig. 4 ). Based on SOTIP detected tumor-immune boundary, we also detected proteins with spatial polarization. In DME analysis, we firstly compared a fibrotic liver sample with healthy liver sample  7  , then identified MECNs specifically enriched in the fibrotic sample. The spatial localization and cellular composition of the detected MECN is consistent with the histology image. We finally applied SOTIP to compare the MECN differences between compartmentalized and mixed subtypes of triple negative breast cancer (TNBC), consistent with previously reported tumorimmune interactions and revealing possible theory to explain the driven factor for the differentiation of these two subtypes.
Specifically, each node is defined as an MECN, which is a bag of cells encoded by cell clusters within the spatial neighborhood. Then each MECN is represented by counting the frequency of each cell cluster (generated by user-defined clustering algorithm, e. g. , Leiden) within the MECN, resulting a histogram. In this way, for a spatial omics dataset of a tissue sample, the number of MECNs is the same as the number of cells, and every MECN are represented by a vector with the length of number of cell clusters. To define the edge between two nodes in MEG, SOTIP computes earth mover's distance (EMD)  88  between them. Considering the cell discrepancy within high-dimensional gene expression space, we derive a connectivity guided minimum graph distance (CGMGD) as the ground distance which approximates the distance in the transcriptome state space.
Simulation datasets There are four simulation datasets used in this study. Simulation 1~3 were firstly generated with Splatter 99 , a R package for scRNA-seq data simulation, then arrange the spatial coordination for the generated cells. Simulation 4 is generated by Splatter as single-cell data, without spatial coordination. The full information for these datasets is summarized in Supplementary Table  2. In the analysis of simulation 3 (Fig. 2e, f ), the relative likelihood of observing each microenvironment in specific sample is performed by MELD  55  , with the precomputed MECN distance matrix as input.
Public datasets This study involved multiple datasets from seven different spatial omics technologies. All datasets are publicly available. Human HeLa cell line 4i dataset: https://squidpy. readthedocs. io/en/stable/  23. Mouse brain cortex osmFISH dataset: http://linnarssonlab. org/osmFISH  46. Mouse brain cortex seqFISH+ dataset: https://github. com/CaiGroup/ seqFISH-PLUS  17. Zebrafish melanoma Visium dataset: GSE159709  61. Human brain cortex Visium dataset: http://research. libd. or g/ spatialLIBD/  48. Human colorectal carcinoma scMEP dataset: https:// zenodo. org/record/3951613  49. Human triple negative breast cancer MIBI dataset: https://mibi-share. ionpath. com/  12. TOF-SIMS liver dataset: https://github. com/yuanzhiyuan/SEAM/tree/master/SEAM/data/ raw_tar  7. The full information of public datasets used in this study can be found in Supplementary Table  3.
Method comparison To evaluate the performance in spatial heterogeneity (SHN) quantification, NUCC and IGD was compared with SOTIP. As with SOTIP, NUCC, IGD both need to perform clustering and define spatial neighborhood. For a fair comparison, NUCC, IGD, and SOTIP utilized exactly the same parameters (MECN size and cluster resolution). We also compared the relative performance under different combinations of these parameters, the parameters were also consistent in every comparison. With 4i dataset (Fig. 3a-f ), since the original data (Supplementary Table  3 ) provided ground truth of nucleus and cytoplasm, we defined their boundary as width of 2 pixels. We used area under curve (AUC) to evaluate and compare the performance. With osmFISH dataset (Fig. 3k ), the original data (Supplementary Table  3 ) provided cell-wise annotations of different cortical layers.
We used Spearman's rank correlation coefficient to evaluate the ordinal agreement between the layer order and the computed SHN. To digitalize the layer order, we set a number for each layer, Pia Layer 1 (1), Layer 2-3 medial (2. 5), Layer 2-3 lateral (2. 5), Layer 3-4 (3. 5), Layer 4 (4), Layer 5 (5), Layer 6 (6). To test the impact of over-clustering on SHN quantification (Supplementary Fig. 2 ), on osmFISH data and seqFISH data, we set the clustering resolution to moderate resolution, over-clustering (3 × moderate), and extreme over-clustering (5 × moderate). The moderate resolution was determined by resolution researching given true number of clusters (provided by original paper  17, 46  ). To evaluate the performance in spatial domain (SDM) identification, for both brain cortex datasets (Fig.
4 ), we set the true number of clusters to run compared algorithms, and used adjusted Rand index (ARI) to compare the similarity between clustering result and ground truth. Note that for human sample, since original ground truth labels contain "N/A" (Fig. 4b ), we filtered out these spots before the comparison. The ARI of the human sample was directly adopted from the ARI as they reported in the original paper  36, 37. We also applied the same gene filtering and data normalization procedures as with code provided by SpaGCN. For the mouse cortex osmFISH dataset, the original ground truth labels contain "excluded" (Fig. 4e ), we filtered out these single cells before the comparison, and the parameter of SpaGCN was set as default. As for the spatial proteomics datasets (Fig. 5 ), the original paper provided ground truth for tumorimmune boundaries, based on which we compared SOTIP and SpaGCN qualitatively.
Acknowledgements This research was supported by the  National Key Research and Development Program of China  ( 2018YFA0801402 ),  National Natural Science Foundation of China  ( 81890994 ) to M. L. S. ,  National Natural Science Foundation of China  ( 81890991 ),  Beijing Municipal Natural Science Foundation  ( Z200021 ),  CAS Interdisciplinary Innovation Team  ( JCTD-2020-04 ), and the  State Key Research Development Program of China  ( 2021YFE0201100 ) to J. T. G. M. Q. Z. acknowledges the support by the  Cecil H. and Ida Green Distinguished  Chair. Z. Y. Y. acknowledges the support by  Shanghai Municipal Science and Technology Major Project  (No. 2018SHZDZX01 ),  ZJ Lab ,  Shanghai Center for Brain Science and Brain-Inspired Technology , and  111 Project  (No. B18015 ).
Data availability All raw data are freely available at following links: Human HeLa cell line (4i): [https://squidpy. readthedocs. io/en/stable/] Mouse Brain cortex (osmFISH): [http://linnarssonlab. org/osmFISH] Mouse Brain cortex (seqFISH+): [https://github. com/CaiGroup/seqFISH-PLUS] Zebrafish melanoma (10X Visium): GSE159709 Human Brain cortex (10X Visium): [http://research. libd. org/spatialLIBD] Human colorectal carcinoma (scMEP): [https://zenodo. org/record/3951613] Human triple-negative breast cancer (MIBI): [https://mibishare. ionpath. com/] Liver (SIMS):.
2019. [https://github. com/yuanzhiyuan/SEAM/] Mouse brain (EASI-FISH): [https://janelia. figshare. com/articles/dataset/EASI-FISH_enabled_ spatial_analysis_of_molecular_cell_types_in_the_lateral_hypothalamus/ 13749154] Human breast cancer (3D IMC): [https://doi. org/10. 5281/ zenodo. 4752030] The processed data in this manuscript can be downloaded at figshare [https://doi. org/10. 6084/m9. figshare. 18516128]. Source data are provided with this paper.
Modeling System preparation. PDB structures of the GlyR-α1 extracted from the initial trajectory (see above) were embedded in a POPC membrane bilayer of 120×120 Å 2 , solvated with TIP3P water molecules (22. 5 Å at the top and the bottom of the protein), and solvated with 150 mM of NaCl, using CHARMM scripts from CHARMM-GUI (51, 52) but executed locally. Concerning the mutants of GlyR-α1, the mutations were introduced by modifying the name of the concerned residues in the initial PDB prior to follow the same procedure of setup with CHARMM (53). The system prepared using these parameters are constituted of about 230k atoms and measured 120×120×170 Å 3. Molecular Dynamics simulations. All-atom MD simulations were run with GROMACS 2019. 4 (54), using periodic boundaries conditions, and the CHARMM36 forcefield  (55, 56)  with CHARMM36m modifications  (57).
The LINCS algorithm was used to constrain bonds involving hydrogens  (61)  and Particle Mesh Ewald (PME) to treat the long-range electrostatic interactions  (62). Computational electrophysiology. To quantify channel conductance in simulation, we introduced a constant electric field E z along the z direction that is perpendicular to the membrane plane. The resulting transmembrane potential V m is proportional to the strength of the electric field and the length of the simulated box L z as E z = V m /L z  (63). Estimates of ionic currents were obtained by counting the number of permeation events per unit of time using the FLUX module in Wordom  (64, 65). Error estimates δ on the calculated current I were obtained assuming a Poisson distribution of the permeation events such that δ = I/ N, with N the number of permeation events  (66).
Finally, channel conductance g was computed as g = I/V m. Ion permeation events through the lateral/apical pathways as well as the number of chloride ions in the vestibule were computed using in-house TCL scripts in VMD  (67). Computational electrophysiology of engineered mutants was carried out at a transmembrane potential of -280 mV. Although non-physiological, the use of a large and negative voltage ensures significant amplitude of the ionic current even in the presence of mutations hindering chloride translocation (e. g. , K104E in Fig. 1 ), which grants for meaningful statistics on the simulation time scale. The effect of the mutation was then quantified by measuring the fraction of the chloride flux exiting the vestibule laterally, here termed lateral permeability ratio, which was computed as the outward chloride permeation rate via the lateral fenestrations over the inward permeation rate across the membrane.
Outside-out recordings. Recording currents are obtained with a RK-400 amplifier (BioLogic) using pClamp 10. 5 software, digitized with a 1550 digidata (Axon instruments). Recording pipettes were obtained from thick-wall borosilicate glass (1. 5 mm × 0. 75 mm × 7. 5 cm, Sutter Instrument) using a micropipettes puller (P-1000, Sutter Instrument) and fire-polished with a micro-forge (MF-830, Narishige) to be used at resistances between 7 and 15 MΩ. Micro-pipettes were filled with internal solution (that contain in mM: 152 NaCl, 1 MgCl 2 , 10 BAPTA, 10 HEPES; pH adjusted to 7. The data show that at negative voltages chloride ions are pumped into the vestibule, whereas at positive voltages the vestibular chloride is depleted. and Eq. A7 in SI, I-V curves for the wild-type receptor (red/green) and the anomalous mutants (black) at both positive and negative voltages were obtained.
Data and materials availability: In-house VMD scripts for counting ion permeation events via the lateral/apical pathways over time and counting the number of chloride ions in the vestibule are provided at the following links: https://doi. org/10. 5281/zenodo. 6935496 https://doi. org/10. 5281/zenodo. 6935478 Molecular snapshots of the zebrafish GlyR-α1 solvated and embedded in a lipid bilayer in the MD-open conformation that were used as starting points for the computational electrophysiology experiments are provided at the following link: https://doi. org/10. 5281/zenodo. 6529095 All other data are available in the main text or the supplementary materials.
I. INTRODUCTION Quantum process tomography (QPT) -the task of estimating an unknown quantum transformation completely from measurement data -is a powerful, but resource-intensive, tool for quantum technology. It has been applied in a variety of experimental contexts  [1] [2] [3] [4] [5] [6]. However, the ongoing growth in size of quantum hardware, such as quantum circuits and simulators, motivates the design of QPT techniques that use relevant resources as sparingly as possible. The earliest QPT proposals  [7, 8]  used linear inversion techniques to reconstruct quantum channels from informationally complete datasets obtained by feeding different (known) input states into the process and performing full quantum state tomography on the resulting outputs. Later, it was realised that by applying the channel-state duality uncovered by Choi  [9]  and Jamiołkowski  [10] , one could perform QPT by simply applying the channel to a maximally entangled state on the system and an ancilla, and using quantum state tomography to reconstruct the channel's Choi matrix directly  [11, 12].
VI. NUMERICAL EXPERIMENTS In this section we outline the results of several computer simulations to illustrate the proposed methods. All the experiments in this section were done on a quad-core Intel Core i3-8100 with 16 GB memory (computation times given in Figure  8 ). Mainly because of memory requirements, the experiments on 7 qubits in Figure  1  were done on 64 cores of Intel Xeon E7-8890 with 512 GB memory, needing around three days for each. The code is available on GitHub  [63]. The repository also contains up-to-date information on the future article on the theoretical underpinnings and heuristics behind HIP  [64].
Our sampling complexity bounds for the Frobenius error depend linearly on the rank r of the channel and are smaller than those of the LS estimator by a factor r/d 2. This qualitative behaviour is confirmed by numerical simulations which show that the PLS errors are significantly lower than those of LS for low rank channels. We carried out several numerical studies involving 5 to 7 qubit channels, including a comparison between the two projection methods, a study on the error dependence on rank, and an analysis of how the computational time scales with system dimension. The code is available on GitHub  [63]. The repository also contains up-to-date information on the future article on the theoretical underpinnings and heuristics behind HIP  [64]. We leave as a topic of future investigations the extension of these results to quantum instruments described in terms of non trace-preserving quantum operations.
In a different direction, we would like to further investigate the efficacy and possible improvement of the confi-dence regions prescribed by Theorem 2. Proof. The proof of this result comes from relating the frequency measurements made in scenarios III A and III B. It relies on the following identity relating the output state C(ρ) of a channel C to the Choi matrix Φ = C(|Ω Ω|) C(ρ) = d × Tr A (Φ (1 ⊗ ρ )). ( 25 ) Using this result, we have that the probability of observing the result p ∈ {0, 1} k when measuring with setting b, having passed in the pure state P a q is: p a b q p = d × Tr(Φ P b p ⊗ P a q ). ( 26 ) Note that up to the factor d, these coincide with the probabilities (3) from scenario III A, with the identifications (a b) = o and (q p) = s. The difference is due to the fact that while in scenario III A both parts (a b) of the outcome o are random, in scenario III B a single dataset is generated from random outcomes b for each deterministically chosen state with labels a and q.
g. ,  Haubrock et al. , 2021a) , there is an urgent need to investigate whether the cost increase is solely due to increased research effort (i. e. , whether costs are increasing at a greater rate than reporting effort). Evidence for these patterns can be identified using the InvaCost database, the largest and most comprehensive global compilation of published costs incurred due to IAS, which offers a sound basis for the synthesis and comparison of monetary costs at several scales  (Diagne et al. , 2020). Using currency as a common global metric, InvaCost provides evidence for much-needed investments to curtail future biological invasions and their impacts  (Ahmed et al. , 2021) , albeit falling short at capturing nonmarket impacts as they are seldom reported in monetary terms  (Hanley and Roberts, 2019).
The InvaCost database includes both damage and management costs, incurred by both primary sectors (e. g. , agriculture, forestry, fisheries) and wider society (e. g. , health, public and social welfare) at a variety of spatial and temporal scales, per the reporting by underlying studies compiled (full list of descriptor variables at doi:https://doi. org/10. 6084/ m9. figshare. 12668570). Within this database, standardisation protocols have enabled the assessment of temporal dynamics in invasion costs across a range of cost descriptors (e. g. , from spatial and taxonomic to sectors of the economy affected). Harnessing these data permits the comparative analysis of temporal trends in invasion costs at global and more granular scales, to identify the countries associated with increasing economic costs from invasions and the taxa driving them.
Yet, trends in the monetary burden posed by IAS and the underlying research effort have not been investigated or linked formally using a comprehensive global dataset. With an increased understanding of the monetary burden posed by IAS, the present study aims to analyse the temporal trends in cost reporting and monetary costs of IAS at continental (regional) and national scales over time. Specifically, we ask: (1) Are costs increasing beyond what we expect due to increasing research effort? (2) Are long-term trends in IAS costs different across geographic regions? (3) If so, to what extent are such trends driven by different taxonomic groups? As a result of ongoing globalisation and the predicted increase in biological invasions  (Seebens et al. , 2021a (Seebens et al. , , 2021b)) , as well as advances in invasion science, we expect to observe: (i) greater increases in the trajectory of monetary costs than that of cost reporting documents across all geographic regions, but (ii) differing taxon contributions to the potential variability of cost increases across regional trajectories.
Data processing As a basis for the analysis, we used the latest available version of the InvaCost database  (Diagne et al. , 2020; Angulo et al. , 2021; version 4, https://doi. org/10. 6084/m9. figshare. 12668570). This database version contains 13,123 cost entries described in a sufficiently detailed manner for large-scale syntheses of costs associated with IAS at different spatial, taxonomic and temporal scales. Following the InvaCost protocol  (Diagne et al. , 2020) , data were mostly retrieved using a series of search strings entered into the Web of Science platform (https://webofknowledge. com/), Google Scholar database (https://scholar. google. com/) and the Google search engine (https://www. google. com/) to identify relevant references with monetary costs of invasions. Full details of the descriptor variables used to compile costs in the database are provided on an open access repository (https://doi.
Despite the challenges in standardising costs and the presence of limitations, InvaCost is the most comprehensive database of reported economic costs of IAS to date that has largely succeeded in addressing issues related to standardisation across time and countries where costs were reported. In addition, this database is public and regularly updated with new cost data as they become known. All costs registered in the database were converted to US$ 2017 values (see  Diagne et al. , 2020  and Supplement 1 for detailed information). An inflation factor was used in the database through division of the Consumer Price Index (https://data. worldbank. org/indicator/FP. CPI. TOTL?end= 2017&start=1960) of 2017 by that of the year of cost estimation. We note that InvaCost also converts costs using purchasing power parity  (Diagne et al.
, 2020 ; https://doi. org/10. 6084/m9. figshare. 12668570), accounting for differences in price level and purchasing power across countries. However, this conversion could not be made for all cost entries, therefore potentially hampering our analysis. Additionally, using purchasing power parity would reduce comparability with other cost papers from InvaCost, which tend to use 2017 US$ based on classical exchange rates  (Cuthbert et al. , 2021 (Cuthbert et al. , , 2022;; Haubrock et al. , 2021a Haubrock et al. , , 2021b;; Diagne et al. , 2021b; Fantle-Lepczyk et al. , 2022) , and results here would be qualitatively the same. Deriving the cumulative cost of invasions over time requires consideration of the duration of each cost occurrence. Entries in the InvaCost database include the adjusted "probable starting" and "probable ending" years, referring to the year range in which the cost was known or assumed to occur, based on details described in the references.