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Here we report pulse voltammetry and operando X-ray absorption spectroscopy measurements on iridium oxide to show that the applied bias does not act directly on the reaction coordinate, but affects the electrocatalytically generated current through charge accumulation in the catalyst. We find that the activation free energy decreases linearly with the amount of oxidative charge stored, and show that this relationship underlies electrocatalytic performance and can be evaluated using measurement and computation. We anticipate that these findings and our methodology will help to better understand other electrocatalytic materials and design systems with improved performance.The modern description of elementary particles, as formulated in the standard model of particle physics, is built on gauge theories1. Gauge theories implement fundamental laws of physics by local symmetry constraints. For example, in quantum electrodynamics Gauss’s law introduces an intrinsic local relation between charged matter and electromagnetic fields, which protects many salient physical properties, including massless photons and a long-ranged Coulomb law. Solving gauge theories using classical computers is an extremely arduous task2, which has stimulated an effort to simulate gauge-theory dynamics in microscopically engineered quantum devices3-6. Previous achievements implemented density-dependent Peierls phases without defining a local symmetry7,8, realized mappings onto effective models to integrate out either matter or electric fields9-12, or were limited to very small systems13-16. However, the essential gauge symmetry has not been observed experimentally. Here we report the quantum simulation of an extended U(1) lattice gauge theory, and experimentally quantify the gauge invariance in a many-body system comprising matter and gauge fields. These fields are realized in defect-free arrays of bosonic atoms in an optical superlattice of 71 sites. We demonstrate full tunability of the model parameters and benchmark the matter-gauge interactions by sweeping across a quantum phase transition. Using high-fidelity manipulation techniques, we measure the degree to which Gauss’s law is violated by extracting probabilities of locally gauge-invariant states from correlated atom occupations. Our work provides a way to explore gauge symmetry in the interplay of fundamental particles using controllable large-scale quantum simulators.The science of cities seeks to understand and explain regularities observed in the world’s major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities. This was first thought to be described by a universal principle known as Zipf’s law1,2; however, the validity of this model has been challenged by recent empirical studies3,4. A theoretical model must also be able to explain the relatively frequent rises and falls of cities and civilizations5, but despite many attempts6-10 these fundamental questions have not yet been satisfactorily answered. Here we introduce a stochastic equation for modelling population growth in cities, constructed from an empirical analysis of recent datasets (for Canada, France, the UK and the USA). This model reveals how rare, but large, interurban migratory shocks dominate city growth. This equation predicts a complex shape for the distribution of city populations and shows that, owing to finite-time effects, Zipf’s law does not hold in general, implying a more complex organization of cities. It also predicts the existence of multiple temporal variations in the city hierarchy, in agreement with observations5. Our result underlines the importance of rare events in the evolution of complex systems11 and, at a more practical level, in urban planning.Stellar mergers are a brief but common phase in the evolution of binary star systems1,2. These events have many astrophysical implications; for example, they may lead to the creation of atypical stars (such as magnetic stars3, blue stragglers4 and rapid rotators5), they play an important part in our interpretation of stellar populations6 and they represent formation channels of compact-object mergers7. Although a handful of stellar mergers have been observed directly8,9, the central remnants of these events were shrouded by an opaque shell of dust and molecules10, making it impossible to observe their final state (for example, as a single merged star or a tighter, surviving binary11). Here we report observations of an unusual, ring-shaped ultraviolet (‘blue’) nebula and the star at its centre, TYC 2597-735-1. DZNeP in vivo The nebula has two opposing fronts, suggesting a bipolar outflow of material from TYC 2597-735-1. The spectrum of TYC 2597-735-1 and its proximity to the Galactic plane suggest that it is an old star, yet it has abnormally low surface gravity and a detectable long-term luminosity decay, which is uncharacteristic for its evolutionary stage. TYC 2597-735-1 also exhibits Hα emission, radial-velocity variations, enhanced ultraviolet radiation and excess infrared emission-signatures of dusty circumstellar disks12, stellar activity13 and accretion14. Combined with stellar evolution models, the observations suggest that TYC 2597-735-1 merged with a lower-mass companion several thousand years ago. TYC 2597-735-1 provides a look at an unobstructed stellar merger at an evolutionary stage between its dynamic onset and the theorized final equilibrium state, enabling the direct study of the merging process.An amendment to this paper has been published and can be accessed via a link at the top of the paper.Dozens of genes contribute to the wide variation in human pigmentation. Many of these genes encode proteins that localize to the melanosome-the organelle, related to the lysosome, that synthesizes pigment-but have unclear functions1,2. Here we describe MelanoIP, a method for rapidly isolating melanosomes and profiling their labile metabolite contents. We use this method to study MFSD12, a transmembrane protein of unknown molecular function that, when suppressed, causes darker pigmentation in mice and humans3,4. We find that MFSD12 is required to maintain normal levels of cystine-the oxidized dimer of cysteine-in melanosomes, and to produce cysteinyldopas, the precursors of pheomelanin synthesis made in melanosomes via cysteine oxidation5,6. Tracing and biochemical analyses show that MFSD12 is necessary for the import of cysteine into melanosomes and, in non-pigmented cells, lysosomes. Indeed, loss of MFSD12 reduced the accumulation of cystine in lysosomes of fibroblasts from patients with cystinosis, a lysosomal-storage disease caused by inactivation of the lysosomal cystine exporter cystinosin7-9.