Protein charge organization is dependent on the low-permittivity region in the hydrophobic core of the molecule. We suggest a novel approach to estimate the dielectric constant of this region by comparing measured and simulated first- and second-order charge moments. Here, the dipole moment is measured as a function of pH using dielectric spectroscopy. The results are compared to dipole moments based on Poisson-Boltzmann estimates of pK(a) shifts calculated from structures in the Protein Data Bank. Structures are additionally refined using CHARMM molecular dynamics simulations. The best estimate for the internal permittivity is found by minimizing the root-mean-square residual between measured and predicted charge moments. Using the protein β-lactoglobulin, a core dielectric constant in the range of 6-7 is estimated.
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately, kernel means are faced with scalability issues. A single point evaluation of the kernel density estimator, for example, requires a computation time linear in the training sample size. To address this challenge, we present a method to efficiently construct a sparse approximation of a kernel mean. We do so by first establishing an incoherence-based bound on the approximation error, and then noticing that, for the case of radial kernels, the bound can be minimized by solving the k-center problem. The outcome is a linear time construction of a sparse kernel mean, which also lends itself naturally to an automatic sparsity selection scheme. We show the computational gains of our method by looking at three problems involving kernel means: Euclidean embedding of distributions, class proportion estimation, and clustering using the mean-shift algorithm.
Dielectric spectroscopy measurements of liquids are often limited by electrode polarization. The influence of surface polishing and deposition of the conducting polymer polypyrrole/polystyrenesulfonate (PPy/PSS) on the polarization impedance is investigated. A quantitative description of the electrode polarization contribution to the real-valued permittivity spectrum is derived. This description explains the origin of the ω(-const). (const.>1) dependency commonly observed in permittivity measurements. Electrode surface roughness is correlated with both the magnitude and phase of the constant phase element. Generally, rougher electrodes have better performance, and an order of magnitude bandwidth improvement is achieved using PPy/PSS electrodes.
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.
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