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Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications because of their unique combination of properties. Upon dissolving alkali metal salts, such as Li or... 

This paper shows that dropout training in generalized linear models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game, nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability δ. This result implies that dropout training indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. The paper makes a concrete recommendation on how to select the tuning parameter δ. The paper also provides a novel, parallelizable, unbiased multi-level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector. 

We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first illustrates the benefits of incorporating a natural geometric structure within a linear regression model, which corresponds to the generalized eigenvalue problem formed by the Gram matrices of both domains. We next establish a finite-sample minimax lower bound, propose a refined model interpolation estimator that enjoys a matching upper bound, and then extend our framework to multiple source domains and generalized linear models. Surprisingly, as long as information is available on the distance between the source and target parameters, negative-transfer does not occur. Simulation studies show that our proposed interpolation estimator outperforms state-of-the-art transfer learning methods in both moderate- and high-dimensional settings. 

ABSTRACT Microbe-mediated transformations of arsenic (As) often require As to be taken up into cells prior to enzymatic reaction. Despite the importance of these microbial reactions for As speciation and toxicity, understanding of how As bioavailability and uptake are regulated by aspects of extracellular water chemistry, notably dissolved organic matter (DOM), remains limited. Whole-cell biosensors utilizing fluorescent proteins are increasingly used for high-throughput quantification of the bioavailable fraction of As in water. Here, we present a mathematical framework for interpreting the time series of biosensor fluorescence as a measure of As uptake kinetics, which we used to evaluate the effects of different forms of DOM on uptake of trivalent arsenite. We found that thiol-containing organic compounds significantly inhibited uptake of arsenite into cells, possibly through the formation of aqueous complexes between arsenite and thiol ligands. While there was no evidence for competitive interactions between arsenite and low-molecular-weight neutral molecules (urea, glycine, and glyceraldehyde) for uptake through the aquaglyceroporin channel GlpF, which mediates transport of arsenite across cell membranes, there was evidence that labile DOM fractions may inhibit arsenite uptake through a catabolite repression-like mechanism. The observation of significant inhibition of arsenite uptake at DOM/As ratios commonly encountered in wetland pore waters suggests that DOM may be an important control on the microbial uptake of arsenite in the environment, with aspects of DOM quality playing an important role in the extent of inhibition. IMPORTANCE The speciation and toxicity of arsenic in environments like rice paddy soils and groundwater aquifers are controlled by microbe-mediated reactions. These reactions often require As to be taken up into cells prior to enzymatic reaction, but there is limited understanding of how microbial arsenic uptake is affected by variations in water chemistry. In this study, we explored the effect of dissolved organic matter (DOM) quantity and quality on microbial As uptake, with a focus on the role of thiol functional groups that are well known to form aqueous complexes with arsenic. We developed a quantitative framework for interpreting fluorescence time series from whole-cell biosensors and used this technique to evaluate effects of DOM on the rates of microbial arsenic uptake. We show that thiol-containing compounds significantly decrease rates of As uptake into microbial cells at environmentally relevant DOM/As ratios, revealing the importance of DOM quality in regulating arsenic uptake, and subsequent biotransformation, in the environment. 

The conditions for rupture of a material commonly vary from sample to sample. Of great importance to applications are the conditions for rare-event rupture, but their measurements require many sam- ples and consume much time. Here, the conditions for rare-event rupture are measured by developing a high-throughput experiment. For each run of the experiment, 1,000 samples are printed under the same nominal conditions and pulled simultaneously to the same stretch. Identifying the rupture of individual samples is automated by processing the video of the experiment. Under monotonic load, the rupture stretch for each sample is recorded. Under cyclic load, the number of cycles to rupture for each sample is also recorded. Rare-event rupture is studied by using the Weibull distribution and the peak-over-threshold method. This work reaffirms that predict- ing rare events requires large datasets. The high-throughput exper- iments enable the prediction of rare events with high accuracy and confidence. 

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited training sample size, is sensitive to noise and may perform poorly on downstream predictive tasks. To mitigate these issues, we propose a distributionally robust maximum likelihood estimator that minimizes the worst-case expected log-loss uniformly over a parametric Kullback-Leibler ball around a parametric nominal distribution. Leveraging the analytical expression of the Kullback-Leibler divergence between two distributions in the same natural exponential family, we show that the min-max estimation problem is tractable in a broad setting, including the robust training of generalized linear models. Our novel robust estimator also enjoys statistical consistency and delivers promising empirical results in both regression and classification tasks.