Identification and Estimation of Causal Effects Using non-Gaussianity and Auxiliary Covariates

Assessing causal effects in the presence of unmeasured confounding is a challenging problem. Although auxiliary variables, such as instrumental variables, are commonly used to identify causal effects, they are often unavailable in practice due to stringent and untestable conditions. To address this issue, previous researches have utilized linear structural equation models to show that the causal effect can be identifiable when noise variables of the treatment and outcome are both non-Gaussian. In this paper, we investigate the problem of identifying the causal effect using auxiliary covariates and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. The auxiliary covariate can be an invalid instrument or an invalid proxy variable. We demonstrate that the causal effect can be identified using this measured covariate, even when the only source of non-Gaussianity comes from the treatment. We then extend the identification results to the multi-treatment setting and provide sufficient conditions for identification. Based on our identification results, we propose a simple and efficient procedure for calculating causal effects and show the $\sqrt{n}$-consistency of the proposed estimator. Finally, we evaluate the performance of our estimator through simulation studies and an application.Comment: 16 papges, 7 Figure

Acoustic Holographic Rendering with Two-dimensional Metamaterial-based Passive Phased Array.

Acoustic holographic rendering in complete analogy with optical holography are useful for various applications, ranging from multi-focal lensing, multiplexed sensing and synthesizing three-dimensional complex sound fields. Conventional approaches rely on a large number of active transducers and phase shifting circuits. In this paper we show that by using passive metamaterials as subwavelength pixels, holographic rendering can be achieved without cumbersome circuitry and with only a single transducer, thus significantly reducing system complexity. Such metamaterial-based holograms can serve as versatile platforms for various advanced acoustic wave manipulation and signal modulation, leading to new possibilities in acoustic sensing, energy deposition and medical diagnostic imaging

An invisibility cloak using silver nanowires

In this paper, we use the parameter retrieval method together with an analytical effective medium approach to design a well-performed invisible cloak, which is based on an empirical revised version of the reduced cloak. The designed cloak can be implemented by silver nanowires with elliptical cross-sections embedded in a polymethyl methacrylate host. This cloak is numerically proved to be robust for both the inner hidden object as well as incoming detecting waves, and is much simpler thus easier to manufacture when compared with the earlier proposed one [Nat. Photon. 1, 224 (2007)].Comment: 7 pages, 4 figures, 2 table

Analysis of the Metals in Soil-Water Interface in a Manganese Mine

In order to reveal the influence of the metals of soil-water interface in a manganese mine (Xiangtan, China), on local water environment, there are six kinds of metals (Mn, Ni, Cu, Zn, Cd, and Pb) characterized by measuring their concentration, correlation, source, and special distribution using principal component analysis, single factor, and Nemero comprehensive pollution index. The results showed that the corresponding average concentration was 0.3358, 0.045, 0.0105, 0.0148, 0.0067, and 0.0389 mg/L. The logarithmic concentration of Mn, Zn, and Pb was normal distribution. The correlation coefficients (between Mn and Pb, Mn and Zn, Mn and Ni, Cu and Zn, Cu and Pb, and Zn and Cd) were found to range from 0.5 to 0.6, and those between Cu and Ni and Cu and Cd were below 0.3. It was found that Zn and Mn pollution were caused primarily by ore mining, mineral waste transportation, tailing slag, and smelting plants, while Cu and Ni mainly originate from the mining industry activities and the traffic transportation in the mining area. In addition, the Cd was considered to be produced primarily from the agricultural or anthropogenic activities. The pollution indexes indicated that metal pollution degree was different in soil-water interface streams as listed in increasing order of pollution level as Zn > Ni > Cu > Pb > Mn > Cd. For all of the pollution of the soil-water interface streams, there was moderate metal pollution but along the eastern mine area the pollution seemed to get more serious. There was only a small amount of soil-water interface streams not contaminated by the metals

Spatial Variability and Distribution of the Metals in Surface Runoff in a Nonferrous Metal Mine

The spatial variation and distribution features of the metals tested in the surface runoff in Xikuangshan Bao Daxing miming area were analyzed by combining statistical methods with a geographic information system (GIS). The results showed that the maximum concentrations of those five kinds of the metals (Sb, Zn, Cu, Pb, and Cd) in the surface runoff of the antimony mining area were lower than the standard value except the concentration of metal Ni. Their concentrations were 497.1, 2.0, 1.8, 22.2, and 22.1 times larger than the standard value, respectively. This metal pollution was mainly concentrated in local areas, which were seriously polluted. The variation coefficient of Sb, Zn, Cu, Ni, Pb, and Cd was between 0.4 to 0.6, wherein the Sb’s spatial variability coefficient is 50.56%, indicating a strong variability. Variation coefficients of the rest of metals were less than 50%, suggesting a moderate variability. The spatial structure analysis showed that the squared correlation coefficient (R2) of the models fitting for Sb, Zn, Cu, Ni, Pb, and Cd was between 0.721 and 0.976; the ratio of the nugget value (C0) to the abutment value (C+C0) was between 0.0767 and 0.559; the semivariogram of Sb, Zn, Ni, and Pb was in agreement with a spherical model, while semivariogram of Cu and Cd was in agreement with Gaussian model, and both had a strong spatial correlation. The trend and spatial distribution indicated that those pollution distributions resulting from Ni, Pb, and Cd are similar, mainly concentrated in both ends of north and south in eastern part. The main reasons for the pollution were attributed to the residents living, transportation, and industrial activities; the Sb distribution was concentrated mainly in the central part, of which the pollution was assigned to the mining and the industrial activity; the pollution distributions of Zn and Cu were similar, mainly concentrated in both ends of north and south as well as in west; the sources of the metals were widely distributed