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Graphene has an extremely high in-plane strength yet considerable out-of-plane softness. High crystalline order of graphene assemblies is desired to utilize their in-plane properties, however, challenged by the easy formation of chaotic wrinkles for the intrinsic softness. Here, we find an intercalation modulated plasticization phenomenon, present a continuous plasticization stretching method to regulate spontaneous wrinkles of graphene sheets into crystalline orders, and fabricate continuous graphene papers with a high Hermans’ order of 0.93. The crystalline graphene paper exhibits superior mechanical (tensile strength of 1.1 GPa, stiffness of 62.8 GPa) and conductive properties (electrical conductivity of 1.1 × 105 S m−1, thermal conductivity of 109.11 W m−1 K−1). We extend the ultrastrong graphene papers to the realistic laminated composites and achieve high strength combining with attractive conductive and electromagnetic shielding performance. The intercalation modulated plasticity is revealed as a vital state of graphene assemblies, contributing to their industrial processing as metals and plastics., Strong but flexible graphene tends to wrinkle, which compromises some properties. Here the authors report a solid plasticization method to prepare continuous graphene papers with high crystalline order, achieving high strength, stiffness, electrical and thermal conductivities.

Biological lignin valorization has emerged as a major solution for sustainable and cost-effective biorefineries. However, current biorefineries yield lignin with inadequate fractionation for bioconversion, yet substantial changes of these biorefinery designs to focus on lignin could jeopardize carbohydrate efficiency and increase capital costs. We resolve the dilemma by designing ‘plug-in processes of lignin’ with the integration of leading pretreatment technologies. Substantial improvement of lignin bioconversion and synergistic enhancement of carbohydrate processing are achieved by solubilizing lignin via lowering molecular weight and increasing hydrophilic groups, addressing the dilemma of lignin- or carbohydrate-first scenarios. The plug-in processes of lignin could enable minimum polyhydroxyalkanoate selling price at as low as $6.18/kg. The results highlight the potential to achieve commercial production of polyhydroxyalkanoates as a co-product of cellulosic ethanol. Here, we show that the plug-in processes of lignin could transform biorefinery design toward sustainability by promoting carbon efficiency and optimizing the total capital cost., The current biorefineries yield lignin with inadequate fractionation for bioconversion, yet substantial changes of these biorefinery designs could jeopardize carbohydrate efficiency and increase capital costs. Here the authors resolve the dilemma by designing ‘plug-in processes of lignin’ to enable economic waste valorization.

Current thermochemical methods to generate H2 include gasification and steam reforming of coal and natural gas, in which anthropogenic CO2 emission is inevitable. If biomass is used as a source of H2, the process can be considered carbon-neutral. Seaweeds are among the less studied types of biomass with great potential because they do not require freshwater. Unfortunately, reaction pathways to thermochemically convert salty and wet biomass into H2 are limited. In this study, a catalytic alkaline thermal treatment of brown seaweed is investigated to produce high purity H2 with substantially suppressed CO2 formation making the overall biomass conversion not only carbon-neutral but also potentially carbon-negative. High-purity 69.69 mmol-H2/(dry-ash-free)g-brown seaweed is produced with a conversion as high as 71%. The hydroxide is involved in both H2 production and in situ CO2 capture, while the Ni/ZrO2 catalyst enhanced the secondary H2 formation via steam methane reforming and water-gas shift reactions., While biomass may serve as a renewable source of carbon-neutral hydrogen, it is challenging both to utilize as-found bio-resources and to suppress CO2 formation. Here, authors convert wet, salty seaweed using alkaline thermal treatment to produce high-purity hydrogen and suppress carbon emission.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

An amendment to this paper has been published and can be accessed via a link at the top of the paper

Recently, we classified the oceans into 30 biogeographic realms based on species’ endemicity. Castro-Insua et al. criticize the choices of dissimilarity coefficients and clustering approaches used in our paper, and reanalyse the data using alternative techniques. Here, we explain how the approaches used in our original paper yield results in line with existing biogeographical knowledge and are robust to alternative methods of analysis. We also repeat the analysis using several similarity coefficients and clustering algorithms, and a neural network theory method. Although each combination of methods produces outputs differing in detail, the overall pattern of realms is similar. The coarse nature of the present boundaries of the realms reflects the limited field data but may be improved with additional data and mapping to environmental variables.

Large amounts of waste heat generated in our fossil-fuel based economy can be converted into useful electric power by using thermoelectric generators. However, the low-efficiency, scarcity, high-cost and poor production scalability of conventional thermoelectric materials are hindering their mass deployment. Nanoengineering has proven to be an excellent approach for enhancing thermoelectric properties of abundant and cheap materials such as silicon. Nevertheless, the implementation of these nanostructures is still a major challenge especially for covering the large areas required for massive waste heat recovery. Here we present a family of nano-enabled materials in the form of large-area paper-like fabrics made of nanotubes as a cost-effective and scalable solution for thermoelectric generation. A case study of a fabric of p-type silicon nanotubes was developed showing a five-fold improvement of the thermoelectric figure of merit. Outstanding power densities above 100 W/m2 at 700 °C are therefore demonstrated opening a market for waste heat recovery., To realize waste heat recovery solutions based on thermoelectricity, high-performance materials with device and manufacturing compatibility are required. Here, the authors demonstrate large-area paper-like nanostructured fabrics consisting of aligned nanotubes with high thermoelectric performance.

In this paper we develop the stability rules for NASICON-structured materials, as an example of compounds with complex bond topology and composition. By first-principles high-throughput computation of 3881 potential NASICON phases, we have developed guiding stability rules of NASICON and validated the ab initio predictive capability through the synthesis of six attempted materials, five of which were successful. A simple two-dimensional descriptor for predicting NASICON stability was extracted with sure independence screening and machine learned ranking, which classifies NASICON phases in terms of their synthetic accessibility. This machine-learned tolerance factor is based on the Na content, elemental radii and electronegativities, and the Madelung energy and can offer reasonable accuracy for separating stable and unstable NASICONs. This work will not only provide tools to understand the synthetic accessibility of NASICON-type materials, but also demonstrates an efficient paradigm for discovering new materials with complicated composition and atomic structure., Sodium super ionic conductors are a class of promising energy storage materials owing to their high ionic conductivity. Here, the authors conducted high throughput calculations to understand the synthetic accessibility of NASICON-type materials and demonstrate an efficient paradigm for discovering new complex materials.

The lunar permanently shadowed regions (PSRs) are expected to host large quantities of water-ice, which are key for sustainable exploration of the Moon and beyond. In the near future, NASA and other entities plan to send rovers and humans to characterize water-ice within PSRs. However, there exists only limited information about the small-scale geomorphology and distribution of ice within PSRs because the orbital imagery captured to date lacks sufficient resolution and/or signal. In this paper, we develop and validate a new method of post-processing LRO NAC images of PSRs. We show that our method is able to reveal previously unseen geomorphological features such as boulders and craters down to 3 meters in size, whilst not finding evidence for surface frost or near-surface ice. Our post-processed images significantly facilitate the exploration of PSRs by reducing the uncertainty of target selection and traverse/mission planning., Nature Communications, 12, ISSN:2041-1723

Donor spins in silicon provide a promising material platform for large scale quantum computing. Excellent electron spin coherence times of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}^{* }=268$$\end{document}T2*=268 μs with fidelities of 99.9% have been demonstrated for isolated phosphorus donors in isotopically pure 28Si, where donors are local-area-implanted in a nanoscale MOS device. Despite robust single qubit gates, realising two-qubit exchange gates using this technique is challenging due to the statistical nature of the dopant implant and placement process. In parallel a precision scanning probe lithography route has been developed to place single donors and donor molecules on one atomic plane of silicon with high accuracy aligned to heavily phosphorus doped silicon in-plane gates. Recent results using this technique have demonstrated a fast (0.8 ns) two-qubit gate with two P donor molecules placed 13 nm apart in natSi. In this paper we demonstrate a single qubit gate with coherent oscillations of the electron spin on a P donor molecule in natSi patterned by scanning tunneling microscope (STM) lithography. The electron spin exhibits excellent coherence properties, with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}$$\end{document}T2 decoherence time of 298 ± 30 μs, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}^{* }$$\end{document}T2* dephasing time of 295 ± 23 ns., Multi-donor molecules in Si provide a promising qubit platform, offering advantages over single donor qubits in terms of performance and fabrication. Here, the authors report a single qubit gate and long coherence times in a P donor molecule qubit in natural Si patterned by scanning tunneling microscope hydrogen lithography.

Networks provide a powerful representation of interacting components within complex systems, making them ideal for visually and analytically exploring big data. However, the size and complexity of many networks render static visualizations on typically-sized paper or screens impractical, resulting in proverbial ‘hairballs’. Here, we introduce a Virtual Reality (VR) platform that overcomes these limitations by facilitating the thorough visual, and interactive, exploration of large networks. Our platform allows maximal customization and extendibility, through the import of custom code for data analysis, integration of external databases, and design of arbitrary user interface elements, among other features. As a proof of concept, we show how our platform can be used to interactively explore genome-scale molecular networks to identify genes associated with rare diseases and understand how they might contribute to disease development. Our platform represents a general purpose, VR-based data exploration platform for large and diverse data types by providing an interface that facilitates the interaction between human intuition and state-of-the-art analysis methods., Data-rich networks can be difficult to interpret beyond a certain size. Here, the authors introduce a platform that uses virtual reality to allow the visual exploration of large networks, while interfacing with data repositories and other analytical methods to improve the interpretation of big data.

Computational flattening algorithms have been successfully applied to X-ray microtomography scans of damaged historical documents, but have so far been limited to scrolls, books, and documents with one or two folds. The challenge tackled here is to reconstruct the intricate folds, tucks, and slits of unopened letters secured shut with “letterlocking,” a practice—systematized in this paper—which underpinned global communications security for centuries before modern envelopes. We present a fully automatic computational approach for reconstructing and virtually unfolding volumetric scans of a locked letter with complex internal folding, producing legible images of the letter’s contents and crease pattern while preserving letterlocking evidence. We demonstrate our method on four letterpackets from Renaissance Europe, reading the contents of one unopened letter for the first time. Using the results of virtual unfolding, we situate our findings within a novel letterlocking categorization chart based on our study of 250,000 historical letters., Here, the authors present a fully automatic computational approach for reconstructing and virtually unfolding volumetric scans of locked letters with complex internal folding, producing legible images of the letter’s contents and crease pattern while preserving letterlocking evidence.

Social networks amplify inequalities by fundamental mechanisms of social tie formation such as homophily and triadic closure. These forces sharpen social segregation, which is reflected in fragmented social network structure. Geographical impediments such as distance and physical or administrative boundaries also reinforce social segregation. Yet, less is known about the joint relationships between social network structure, urban geography, and inequality. In this paper we analyze an online social network and find that the fragmentation of social networks is significantly higher in towns in which residential neighborhoods are divided by physical barriers such as rivers and railroads. Towns in which neighborhoods are relatively distant from the center of town and amenities are spatially concentrated are also more socially segregated. Using a two-stage model, we show that these urban geography features have significant relationships with income inequality via social network fragmentation. In other words, the geographic features of a place can compound economic inequalities via social networks., Not much is known about the joint relationships between social network structure, urban geography, and inequality. Here, the authors analyze an online social network and find that the fragmentation of social networks is significantly higher in towns in which residential neighborhoods are divided by physical barriers such as rivers and railroads.

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-21647-w

Oxford Nanopore (ONT) is a leading long-read technology which has been revolutionizing transcriptome analysis through its capacity to sequence the majority of transcripts from end-to-end. This has greatly increased our ability to study the diversity of transcription mechanisms such as transcription initiation, termination, and alternative splicing. However, ONT still suffers from high error rates which have thus far limited its scope to reference-based analyses. When a reference is not available or is not a viable option due to reference-bias, error correction is a crucial step towards the reconstruction of the sequenced transcripts and downstream sequence analysis of transcripts. In this paper, we present a novel computational method to error correct ONT cDNA sequencing data, called isONcorrect. IsONcorrect is able to jointly use all isoforms from a gene during error correction, thereby allowing it to correct reads at low sequencing depths. We are able to obtain a median accuracy of 98.9–99.6%, demonstrating the feasibility of applying cost-effective cDNA full transcript length sequencing for reference-free transcriptome analysis., Nanopore sequencing technologies applied to transcriptome analysis suffer from high error rates, limiting them largely to reference-based analyses. Here, the authors develop a computational error correction method for transcriptome analysis that reduces the median error rate from ~7% to ~1%.

For over ten years, China has been the largest vehicle market in the world. In order to address energy security and air quality concerns, China issued the Dual Credit policy to improve vehicle efficiency and accelerate New Energy Vehicle adoption. In this paper, a market-penetration model is combined with a vehicle fleet model to assess implications on greenhouse gas (GHG) emissions and energy demand. Here we use this integrated modeling framework to study several scenarios, including hypothetical policy tweaks, oil price, battery cost and charging infrastructure for the Chinese passenger vehicle fleet. The model shows that the total GHGs of the Chinese passenger vehicle fleet are expected to peak in 2032 under the Dual Credit policy. A significant reduction in GHG emissions is possible if more efficient internal combustion engines continue to be part of the technology mix in the short term with more New Energy Vehicle penetration in the long term., China issued the Dual Credit policy to improve vehicle efficiency and accelerate new energy vehicle adoption. Here the authors show that the total Greenhouse gas emissions (GHGs) of the Chinese passenger vehicle fleet are expected to peak in 2032 and a significant reduction in GHG emissions is possible by optimizing the Dual Credit policy.

Thousands of functional magnetic resonance imaging (fMRI) studies have provided important insight into the human brain. However, only a handful of these studies tested infants while they were awake, because of the significant and unique methodological challenges involved. We report our efforts to address these challenges, with the goal of creating methods for awake infant fMRI that can reveal the inner workings of the developing, preverbal mind. We use these methods to collect and analyze two fMRI datasets obtained from infants during cognitive tasks, released publicly with this paper. In these datasets, we explore and evaluate data quantity and quality, task-evoked activity, and preprocessing decisions. We disseminate these methods by sharing two software packages that integrate infant-friendly cognitive tasks and eye-gaze monitoring with fMRI acquisition and analysis. These resources make fMRI a feasible and accessible technique for cognitive neuroscience in awake and behaving human infants., Using fMRI on awake infants could help us understand the contents of a baby’s mind, long before they can speak. Here, the authors report advances in how to collect, preprocess, and analyze task-based fMRI data from infants, and they share the resulting datasets and software.

10 páginas.- 3 figuras.- 1 tabla.- 47 referencias.- Supplementary information is available for this paper at https://doi.org/10.1038/s41467-020-17960-5, Ecologists have long argued that higher functioning in diverse communities arises from the niche differences stabilizing species coexistence and from the fitness differences driving competitive dominance. However, rigorous tests are lacking. We couple field-parameterized models of competition between 10 annual plant species with a biodiversity-functioning experiment under two contrasting environmental conditions, to study how coexistence determinants link to biodiversity effects (selection and complementarity). We find that complementarity effects positively correlate with niche differences and selection effects differences correlate with fitness differences. However, niche differences also contribute to selection effects and fitness differences to complementarity effects. Despite this complexity, communities with an excess of niche differences (where niche differences exceeded those needed for coexistence) produce more biomass and have faster decomposition rates under drought, but do not take up nutrients more rapidly. We provide empirical evidence that the mechanisms determining coexistence correlate with those maximizing ecosystem functioning., O.G. acknowledges postdoctoral financial support provided by the European Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 661118-BioFUNC.

Bond dissociation enthalpies (BDEs) of organic molecules play a fundamental role in determining chemical reactivity and selectivity. However, BDE computations at sufficiently high levels of quantum mechanical theory require substantial computing resources. In this paper, we develop a machine learning model capable of accurately predicting BDEs for organic molecules in a fraction of a second. We perform automated density functional theory (DFT) calculations at the M06-2X/def2-TZVP level of theory for 42,577 small organic molecules, resulting in 290,664 BDEs. A graph neural network trained on a subset of these results achieves a mean absolute error of 0.58 kcal mol−1 (vs DFT) for BDEs of unseen molecules. We further demonstrate the model on two applications: first, we rapidly and accurately predict major sites of hydrogen abstraction in the metabolism of drug-like molecules, and second, we determine the dominant molecular fragmentation pathways during soot formation., Bond dissociation enthalpies are key quantities in determining chemical reactivity, their computations with quantum mechanical methods being highly demanding. Here the authors develop a machine learning approach to calculate accurate dissociation enthalpies for organic molecules with sub-second computational cost.

Social networks shape perceptions by exposing people to the actions and opinions of their peers. However, the perceived popularity of a trait or an opinion may be very different from its actual popularity. We attribute this perception bias to friendship paradox and identify conditions under which it appears. We validate the findings empirically using Twitter data. Within posts made by users in our sample, we identify topics that appear more often within users’ social feeds than they do globally among all posts. We also present a polling algorithm that leverages the friendship paradox to obtain a statistically efficient estimate of a topic’s global prevalence from biased individual perceptions. We characterize the polling estimate and validate it through synthetic polling experiments on Twitter data. Our paper elucidates the non-intuitive ways in which the structure of directed networks can distort perceptions and presents approaches to mitigate this bias., Individuals within social networks rarely observe the network as a whole; rather, their observations are limited to their social circles. Here we show that network structure can distort observations, making a trait appear far more common within many social circles than it is in the network as a whole.

In a seminal paper, Mahan predicted that excitonic bound states can still exist in a semiconductor at electron-hole densities above the insulator-to-metal Mott transition. However, no clear evidence for this exotic quasiparticle, dubbed Mahan exciton, exists to date at room temperature. In this work, we combine ultrafast broadband optical spectroscopy and advanced many-body calculations to reveal that organic-inorganic lead-bromide perovskites host Mahan excitons at room temperature. Persistence of the Wannier exciton peak and the enhancement of the above-bandgap absorption are observed at all achievable photoexcitation densities, well above the Mott density. This is supported by the solution of the semiconductor Bloch equations, which confirms that no sharp transition between the insulating and conductive phase occurs. Our results demonstrate the robustness of the bound states in a regime where exciton dissociation is otherwise expected, and offer promising perspectives in fundamental physics and in room-temperature applications involving high densities of charge carriers., The Mahan exciton, exotic quasiparticle predicted in 1967, had never been found in room temperature semiconductors. With ultrafast optics and many-body theory, Palmieri et al. show that methylammonium lead bromide perovskites are ideal platforms to unveil Mahan exciton physics at room temperature.

A membrane with both high ion conductivity and selectivity is critical to high power density and low-cost flow batteries, which are of great importance for the wide application of renewable energies. The trade-off between ion selectivity and conductivity is a bottleneck of ion conductive membranes. In this paper, a thin-film composite membrane with ultrathin polyamide selective layer is found to break the trade-off between ion selectivity and conductivity, and dramatically improve the power density of a flow battery. As a result, a vanadium flow battery with a thin-film composite membrane achieves energy efficiency higher than 80% at a current density of 260 mA cm−2, which is the highest ever reported to the best of our knowledge. Combining experiments and theoretical calculation, we propose that the high performance is attributed to the proton transfer via Grotthuss mechanism and Vehicle mechanism in sub-1 nm pores of the ultrathin polyamide selective layer., Low-cost flow batteries with high power density are promising for energy storage, but membranes with simultaneously high ion conductivity and selectivity should be developed. Here the authors report a thin-film composite membrane that breaks the trade-off between ion conductivity and selectivity.

Direct printing of functional inks is critical for applications in diverse areas including electrochemical energy storage, smart electronics and healthcare. However, the available printable ink formulations are far from ideal. Either surfactants/additives are typically involved or the ink concentration is low, which add complexity to the manufacturing and compromises the printing resolution. Here, we demonstrate two types of two-dimensional titanium carbide (Ti3C2Tx) MXene inks, aqueous and organic in the absence of any additive or binary-solvent systems, for extrusion printing and inkjet printing, respectively. We show examples of all-MXene-printed structures, such as micro-supercapacitors, conductive tracks and ohmic resistors on untreated plastic and paper substrates, with high printing resolution and spatial uniformity. The volumetric capacitance and energy density of the all-MXene-printed micro-supercapacitors are orders of magnitude greater than existing inkjet/extrusion-printed active materials. The versatile direct-ink-printing technique highlights the promise of additive-free MXene inks for scalable fabrication of easy-to-integrate components of printable electronics., Printing functional inks is attractive for applications in electrochemical energy storage and smart electronics, among others. Here the authors report highly concentrated, additive-free, aqueous and organic MXene-based inks that can be used for high-resolution extrusion and inkjet printing.

Nearly two decades of intense study have passed since the term metamaterials was first introduced in 1999. In spite of their great promise, however, metamaterials have been slow to find their way into practical devices, and examples of real-world applications remain rare. In this paper, an Advanced Short Backfire Antenna (A-SBFA), augmented with anisotropic metamaterial surfaces (metasurfaces), has been designed to achieve a very high aperture efficiency across two frequency bands. This performance is unprecedented for an antenna that has seen widespread use, but few design changes over its more than 50 year existence. The reduced weight, compact design, hexagonal aperture, high dual-band efficiency, high cross-polarization isolation, as well as low multipaction and passive intermodulation (PIM) risk make the A-SBFA ideal for spaceborne applications. This transformative design demonstrates how practical metamaterials, when applied to conventional antenna technology, can provide significant performance enhancements., There is significant interest in providing real-world applications for metamaterials. Here, the authors design an Advanced Short Backfire Antenna, augmented with anisotropic metamaterial surfaces to achieve high aperture efficiency across two frequency bands, making the antenna ideal for spaceborne applications.

This paper reports co-crystallization of two atomically precise, different-size ligand-stabilized nanoclusters, a spherical (AuAg)267(SR)80 and a smaller trigonal-prismatic (AuAg)45(SR)27(PPh3)6 in 1:1 ratio, characterized fully by X-ray crystallographic analysis (SR = 2,4-SPhMe2). The larger cluster has a four concentric-shell icosahedral structure of Ag@M12@M42@M92@Ag120(SR)80 (M = Au or Ag) with the inner-core M147 icosahedron observed here for metal nanoparticles. The cluster has an open electron shell of 187 delocalized electrons, fully metallic, plasmonic behavior, and a zero HOMO-LUMO energy gap. The smaller cluster has an 18-electron shell closing, a notable HOMO-LUMO energy gap and a molecule-like optical spectrum. This is the first direct demonstration of the simultaneous presence of competing effects (closing of atom vs. electron shells) in nanocluster synthesis and growth, working together to form a co-crystal of different-sized clusters. This observation suggests a strategy that may be helpful in the design of other nanocluster systems via co-crystallization., Atomic shell closure and electronic shell closure are generally considered to be competing effects in stabilizing magic-sized metal nanoclusters. Here, the authors show, by co-crystallizing two differently-sized clusters, that both mechanisms can work concurrently during magic cluster synthesis.

Visualization and exploration of high-dimensional data is a ubiquitous challenge across disciplines. Widely used techniques such as principal component analysis (PCA) aim to identify dominant trends in one dataset. However, in many settings we have datasets collected under different conditions, e.g., a treatment and a control experiment, and we are interested in visualizing and exploring patterns that are specific to one dataset. This paper proposes a method, contrastive principal component analysis (cPCA), which identifies low-dimensional structures that are enriched in a dataset relative to comparison data. In a wide variety of experiments, we demonstrate that cPCA with a background dataset enables us to visualize dataset-specific patterns missed by PCA and other standard methods. We further provide a geometric interpretation of cPCA and strong mathematical guarantees. An implementation of cPCA is publicly available, and can be used for exploratory data analysis in many applications where PCA is currently used., Dimensionality reduction and visualization methods lack a principled way of comparing multiple datasets. Here, Abid et al. introduce contrastive PCA, which identifies low-dimensional structures enriched in one dataset compared to another and enables visualization of dataset-specific patterns.