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Genetic association signals have been mostly found in noncoding regions through genome-wide association studies (GWAS), suggesting the roles of gene expression regulation in human diseases and traits. However, there has been limited success in colocalizing expression quantitative trait locus (eQTL) with disease-associated variants. Mediated expression score regression (MESC) is a recently proposed method to quantify the proportion of trait heritability mediated by genetically regulated gene expressions (GReX). Applications of MESC to GWAS results have yielded low estimation of mediated heritability for many traits. As MESC relies on stringent independence assumptions between cis-eQTL effects, gene effects, and nonmediated SNP effects, it may fail to characterize the true relationships between those effect sizes, which leads to biased results. Here, we consider the robustness of MESC to investigate whether the low fraction of mediated heritability inferred by MESC reflects biological reality for complex traits or is an underestimation caused by model misspecifications. Our results suggest that MESC may lead to biased estimates of mediated heritability with misspecification of gene annotations leading to underestimation, whereas misspecification of SNP annotations may lead to overestimation. Furthermore, errors in eQTL effect estimates may lead to underestimation of mediated heritability.

 

A deep neural network using rectified linear units represents a continuous piecewise linear (CPWL) function and vice versa. Recent results in the literature estimated that the number of neurons needed to exactly represent any CPWL function grows exponentially with the number of pieces or exponentially in terms of the factorial of the number of distinct linear components. Moreover, such growth is amplified linearly with the input dimension. These existing results seem to indicate that the cost of representing a CPWL function is expensive. In this paper, we propose much tighter bounds and establish a polynomial time algorithm to find a network satisfying these bounds for any given CPWL function. We prove that the number of hidden neurons required to exactly represent any CPWL function is at most a quadratic function of the number of pieces. In contrast to all previous results, this upper bound is invariant to the input dimension. Besides the number of pieces, we also study the number of distinct linear components in CPWL functions. When such a number is also given, we prove that the quadratic complexity turns into bilinear, which implies a lower neural complexity because the number of distinct linear components is always not greater than the minimum number of pieces in a CPWL function. When the number of pieces is unknown, we prove that, in terms of the number of distinct linear components, the neural complexities of any CPWL function are at most polynomial growth for low-dimensional inputs and factorial growth for the worst-case scenario, which are significantly better than existing results in the literature. 

Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, the models fundamentally considered in the literature have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual representation from standard ResNets. We show that wide ResNEsts with bottleneck blocks can always guarantee a very desirable training property that standard ResNets aim to achieve, i.e., adding more blocks does not decrease performance given the same set of basis elements. To prove that, we first recognize ResNEsts are basis function models that are limited by a coupling problem in basis learning and linear prediction. Then, to decouple prediction weights from basis learning, we construct a special architecture termed augmented ResNEst (A-ResNEst) that always guarantees no worse performance with the addition of a block. As a result, such an A-ResNEst establishes empirical risk lower bounds for a ResNEst using corresponding bases. Our results demonstrate ResNEsts indeed have a problem of diminishing feature reuse; however, it can be avoided by sufficiently expanding or widening the input space, leading to the above-mentioned desirable property. Inspired by the densely connected networks (DenseNets) that have been shown to outperform ResNets, we also propose a corresponding new model called Densely connected Nonlinear Estimator (DenseNEst). We show that any DenseNEst can be represented as a wide ResNEst with bottleneck blocks. Unlike ResNEsts, DenseNEsts exhibit the desirable property without any special architectural re-design. 

In thermionic energy converters, the absolute efficiency can be increased up to 40% if space-charge losses are eliminated by using a sub-10-µm gap between the electrodes. One practical way to achieve such small gaps over large device areas is to use a stiff and thermally insulating spacer between the two electrodes. We report on the design, fabrication and characterization of thin-film alumina-based spacers that provided robust 3–8 μm gaps between planar substrates and had effective thermal conductivities less than those of aerogels. The spacers were fabricated on silicon molds and, after release, could be manually transferred onto any substrate. In large-scale compression testing, they sustained compressive stresses of 0.4–4 MPa without fracture. Experimentally, the thermal conductance was 10–30 mWcm⁻²K⁻¹and, surprisingly, independent of film thickness (100–800 nm) and spacer height. To explain this independence, we developed a model that includes the pressure-dependent conductance of locally distributed asperities and sparse contact points throughout the spacer structure, indicating that only 0.1–0.5% of the spacer-electrode interface was conducting heat. Our spacers show remarkable functionality over multiple length scales, providing insulating micrometer gaps over centimeter areas using nanoscale films. These innovations can be applied to other technologies requiring high thermal resistance in small spaces, such as thermophotovoltaic converters, insulation for spacecraft and cryogenic devices.