Lasso adjustments of treatment effect estimates in randomized experiments

We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the Lasso may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman-Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and OLS for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS

Determination of the star valency of a graph

AbstractThe star valency of a graph G is the minimum, over all star decompositions π, of the maximum number of elements in π incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either ⌈dmax-ave(G)/2⌉ or ⌈dmax-ave(G)/2⌉+1, and provide a polynomial time algorithm for determining the star valency of a graph

Integration of surface science, nanoscience, and catalysis

This is the published version. Copyright 2010 International Union of Pure and Applied ChemistryThis article briefly reviews the development of surface science and its close relevance to nanoscience and heterogeneous catalysis. The focus of this article is to highlight the importance of nanoscale surface science for understanding heterogeneous catalysis performing at solid–gas and solid–liquid interfaces. Surface science has built a foundation for the understanding of catalysis based on the studies of well-defined single-crystal catalysts in the past several decades. Studies of catalysis on well-defined nanoparticles (NPs) significantly promoted the understanding of catalytic mechanisms to an unprecedented level in the last decade. To understand reactions performed on catalytic active sites at nano or atomic scales and thus reach the goal of catalysis by design, studies of the surface of nanocatalysts are crucial. The challenges in such studies are discussed

An electron acceptor molecule in a nanomesh: F4TCNQ on h-BN/Rh(111)

The adsorption of molecules on surfaces affects the surface dipole and thus changes in the work function may be expected. The effect in change of work function is particularly strong if charge between substrate and adsorbate is involved. Here we report the deposition of a strong electron acceptor molecule, tetrafluorotetracyanoquinodimethane C$_{12}$F$_4$N$_4$ (F$_{4}$TCNQ) on a monolayer of hexagonal boron nitride nanomesh ($h$-BN on Rh(111)). The work function of the F$_{4}$TCNQ/$h$-BN/Rh system increases upon increasing molecular coverage. The magnitude of the effect indicates electron transfer from the substrate to the F$_{4}$TCNQ molecules. Density functional theory calculations confirm the work function shift and predict doubly charged F$_{4}$TCNQ$^{2-}$ in the nanomesh pores, where the $h$-BN is closest to the Rh substrate, and to have the largest binding energy there. The preferred adsorption in the pores is conjectured from a series of ultraviolet photoelectron spectroscopy data, where the $\sigma$ bands in the pores are first attenuated. Scanning tunneling microscopy measurements indicate that F$_{4}$TCNQ molecules on the nanomesh are mobile at room temperature, as "hopping" between neighboring pores is observed