We report an in situ observation of water condensation and evaporation on lotus leaf surfaces inside an environmental scanning electron microscope. The real-time observation shows, at the micrometer length scale, how water drops grow to large contact angles during water condensation, and decrease in size and contact angle during the evaporation phase of the experiment. To rationalize the observations, we propose a geometric model for liquid drops on rough surfaces when the size of the drop and surface roughness scale are comparable. This model suggests that when drop size and surface roughness are of the same magnitude, such as micrometer size water drops on lotus leaves, well-known equations for wetting on rough surfaces may not be applicable.

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Pulsed field gradient (PFG) NMR at high field was utilized to directly observe a transition between two different diffusion regimes in a Nafion 117 membrane loaded with water and acetone. Although water selfdiffusivity at small water loadings was observed to be diffusion timeindependent in the limit of small and large diffusion times, it showed a significant decrease with increasing diffusion time at intermediate times corresponding to root mean square displacements on the order of several microns. Under our experimental conditions, no self-diffusivity dependence on diffusion time was found for water at large water loadings and for acetone at all studied acetone loadings. The diffusion time-dependent self-diffusivity at small water concentration is explained by the existence of finite domains of interconnected water channels with sizes in the range of several microns that form in Nafion in the presence of acetone. The domain sizes and permeance of transport barriers separating adjacent domains are estimated based on the measured PFG NMR data. At large water concentrations, the water channels form a fully interconnected network, resulting in time-independent self-diffusivity. The absence of such a percolation-like transition with increasing molecular concentration for acetone is attributed to a difference in the regions available for water and acetone diffusion in Nafion. The diffusion data are correlated with and supported by structural data obtained using small-angle X-ray and neutron scattering techniques. These techniques reveal distinct water channels with radial dimensions in the nanometer range increasing upon water addition, while acetone appears to be in an interfacial perfluoroether region, reducing the size of the radial channel dimension.

A novel synthesis technique has been developed that yields monodisperse Pt particles in electrostatically stabilized suspensions without the use of structure directing organic surfactants. The approach uses stannous chloride as both reducing and stabilizing agent to form multifaceted Pt single crystal nanoparticles and clusters of less than 20 atoms. These particles may be assembled into layered electrode structures having well-controlled Pt loadings without precipitation onto organic supports or sintering to remove organic residues, both of which are known to yield particle aggregation and the formation of nonregular structures. Consequently, the particles may be used for fundamental investigations on the effect of platinum dispersion on catalytic activity never previously possible. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) of these particles provides the first direct evidence that peak oxygen reduction reaction (ORR) activity with increased catalyst dispersion is associated with the crystal to cluster transition and a change in reaction mechanism as reflected by the change in the Tafel slope from 120 mV/decade for the crystals to 220 mV/decade for the clusters at high current density. ORR mass activities obtained at 0.9 V versus reversible hydrogen electrode (RHE) from rotating disk electrode (RDE) experiments in perchloric acid were found to systematically vary from a minimum of about 18 A/g for the atomic clusters, to about 48 A/g for the single crystals, to a peak activity of 74 A/g for transitional structures (twice the value measured on commercial catalyst). Furthermore, the peak electrochemically active area (ECA) obtained from proton underpotential deposition is found to occur well within the atomic cluster regime.

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Convolutional image classifiers can achieve high predictive accuracy, but quantifying their uncertainty remains an unresolved challenge, hindering their deployment in consequential settings. Existing uncertainty quantification techniques, such as Platt scaling, attempt to calibrate the network's probability estimates, but they do not have formal guarantees. We present an algorithm that modifies any classifier to output a predictive set containing the true label with a user-specified probability, such as 90%. The algorithm is simple and fast like Platt scaling, but provides a formal finite-sample coverage guarantee for every model and dataset. Furthermore, our method generates much smaller predictive sets than alternative methods, since we introduce a regularizer to stabilize the small scores of unlikely classes after Platt scaling. In experiments on both Imagenet and Imagenet-V2 with ResNet-152 and other classifiers, our scheme outperforms existing approaches, achieving exact coverage with sets that are often factors of 5 to 10 smaller.

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While improving prediction accuracy has been the focus of machine learning in recent years, this alone does not suffice for reliable decision-making. Deploying learning systems in consequential settings also requires calibrating and communicating the uncertainty of predictions. To convey instance-wise uncertainty for prediction tasks, we show how to generate set-valued predictions from a black-box predictor that control the expected loss on future test points at a user-specified level. Our approach provides explicit finite-sample guarantees for any dataset by using a holdout set to calibrate the size of the prediction sets. This framework enables simple, distribution-free, rigorous error control for many tasks, and we demonstrate it in five large-scale machine learning problems: (1) classification problems where some mistakes are more costly than others; (2) multi-label classification, where each observation has multiple associated labels; (3) classification problems where the labels have a hierarchical structure; (4) image segmentation, where we wish to predict a set of pixels containing an object of interest; and (5) protein structure prediction. Lastly, we discuss extensions to uncertainty quantification for ranking, metric learning and distributionally robust learning. * equal contribution see project website at angelopoulos.ai/blog/posts/rcps/