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

Low Rank Directed Acyclic Graphs and Causal Structure Learning

Despite several important advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In particular, the recent formulation of structure learning as a continuous optimization problem proved to have considerable advantages over the traditional combinatorial formulation, but the performance of the resulting algorithms is still wanting when the target graph is relatively large and dense. In this paper we propose a novel approach to mitigate this problem, by exploiting a low rank assumption regarding the (weighted) adjacency matrix of a DAG causal model. We establish several useful results relating interpretable graphical conditions to the low rank assumption, and show how to adapt existing methods for causal structure learning to take advantage of this assumption. We also provide empirical evidence for the utility of our low rank algorithms, especially on graphs that are not sparse. Not only do they outperform state-of-the-art algorithms when the low rank condition is satisfied, the performance on randomly generated scale-free graphs is also very competitive even though the true ranks may not be as low as is assumed

And\^o dilations for a pair of commuting contractions: two explicit constructions and functional models

One of the most important results in operator theory is And\^o's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit constructions (Sch\"affer \cite{sfr} and Douglas \cite{Doug-Dilation}) of the minimal isometric dilation of a single contraction, there was no such explicit construction of an And\^o dilation for a commuting pair $(T_1,T_2)$ of contractions, except in some special cases \cite{A-M-Dist-Var, D-S, D-S-S}. In this paper, we give two new proofs of And\^o's dilation theorem by giving both Sch\"affer-type and Douglas-type explicit constructions of an And\^o dilation with function-theoretic interpretation, for the general case. The results, in particular, give a complete description of all possible factorizations of a given contraction $T$ into the product of two commuting contractions. Unlike the one-variable case, two minimal And\^o dilations need not be unitarily equivalent. However, we show that the compressions of the two And\^o dilations constructed in this paper to the minimal dilation spaces of the contraction $T_1T_2$, are unitarily equivalent. In the special case when the product $T=T_1T_2$ is pure, i.e., if $T^{* n}\to 0$ strongly, an And\^o dilation was constructed recently in \cite{D-S-S}, which, as this paper will show, is a corollary to the Douglas-type construction. We define a notion of characteristic triple for a pair of commuting contractions and a notion of coincidence for such triples. We prove that two pairs of commuting contractions with their products being pure contractions are unitarily equivalent if and only if their characteristic triples coincide. We also characterize triples which qualify as the characteristic triple for some pair $(T_1,T_2)$ of commuting contractions such that $T_1T_2$ is a pure contraction.Comment: 24 page

BeiDou Satellites Assistant Determination by Receiving Other GNSS Downlink Signals

GNSS’s orbit determinations always rely on ground station or intersatellite links (ISL). In the emergency of satellite-to-ground links and ISL break-off, BeiDou navigation satellite system (BDS) satellites cannot determine their orbits. In this paper, we propose to add a spaceborne annular beam antenna for receiving the global positioning system (GPS) and global navigation satellite system (GLONASS) signals; therefore, the BDS satellites may be capable of determining their orbits by GPS/GLONASS signals. Firstly, the spectrum selection, the power isolation, the range of Doppler frequency shift, and changing rate are taken into account for the feasibility. Specifically, the L2 band signals are chosen for receiving and processing in order to prevent the overlapping of the receiving and transmitting signals. Secondly, the minimum number of visible satellites (MNVS), carrier-to-noise ratio (C/N0), dilution of precision (GDOP), and geometric distance root-mean-square (gdrms) are evaluated for acquiring the effective receiving antennas’ coverage ranges. Finally, the scheme of deploying 3 receiving antennas is proved to be optimal by analysis and simulations over the middle earth orbit (MEO), geostationary earth orbit (GEO), and the inclined geosynchronous satellite orbit (IGSO). The antennas’ structures and patterns are designed to draw a conclusion that installing GPS and GLONASS receivers on BDS satellites for emergent orbits determination is cost-effective

Superconducting Diode Effect and Large Magnetochiral Anisotropy in Td_d-MoTe2_2 Thin Film

In the absence of time-reversal invariance, metals without inversion symmetry may exhibit nonreciprocal charge transport -- a magnetochiral anisotropy that manifests as unequal electrical resistance for opposite current flow directions. If superconductivity also sets in, the charge transmission may become dissipationless in one direction while remaining dissipative in the opposite, thereby realizing a superconducting diode. Through both direct-current and alternating-current measurements, we study the nonreciprocal effects in thin films of the noncentrosymmetric superconductor T$_d$-MoTe\textsubscript{2} with disorders. We observe nonreciprocal superconducting critical currents with a diode efficiency close to 20\%~, and a large magnetochiral anisotropy coefficient up to \SI{5.9e8}{\per\tesla\per\ampere}, under weak out-of-plane magnetic field in the millitesla range. The great enhancement of rectification efficiency under out-of-plane magnetic field is likely abscribed to the vortex ratchet effect, which naturally appears in the noncentrosymmetric superconductor with disorders. Intriguingly, unlike the finding in Rashba systems, the strongest in-plane nonreciprocal effect does not occur when the field is perpendicular to the current flow direction. We develop a phenomenological theory to demonstrate that this peculiar behavior can be attributed to the asymmetric structure of spin-orbit coupling in T$_d$-MoTe\textsubscript{2}. Our study highlights how the crystallographic symmetry critically impacts the nonreciprocal transport, and would further advance the research for designing the superconducting diode with the best performance.Comment: 7 pages, 5figure

Milk Consumption and Cardiovascular Risk Factors in Older Chinese: The Guangzhou Biobank Cohort Study

BackgroundDairy products consumption is increasingly common globally. Most of the evidence concerning dairy products comes from observational studies in western populations which are inevitably open to confounding. To triangulate the evidence concerning dairy products, we examined the associations of whole cow’s milk consumption with cardiovascular risk factors in a non-Western setting with a different pattern of milk consumption and cardiovascular diseases from Western populations. MethodsWe used multivariable censored linear or logistic regression to examine cross-sectionally the adjusted associations of whole cow’s milk consumption (none (n = 14892), 1–3/week (n = 2689) and 3+/week (n = 2754)) with cardiovascular risk factors in Chinese ($50 years) in the Guangzhou Biobank Cohort Study. ResultsWhole cow’s milk consumption was negatively associated with systolic blood pressure (3+/week compared to none 22.56 mmHg, 95% confidence interval (CI) 23.63 to 21.49), diastolic blood pressure (21.32 mmHg, 95% CI 21.87 to 20.77) and triglycerides (20.06 mmol/L, 95% CI 20.11 to 20.002), but was positively associated with HDL-cholesterol (0.02 mmol/L,95% CI 0.01 to 0.04) and fasting glucose (0.08 mmol/L, 95% CI 0.01 to 0.16) adjusted for age, sex, phase of study, socio-economic position, lifestyle (smoking, alcohol use and physical activity) and adiposity, but had no obvious association with LDL-cholesterol or the presence of diabetes. ConclusionsWhole cow’s milk consumption had heterogeneous associations with cardiovascular risk factors. Higher whole cow’s milk consumption was associated with lower levels of specific cardiovascular risk factors which might suggest risk factor specific biological pathways with different relations to blood pressure and lipids than glucose

A broad-spectrum gas sensor based on correlated two-dimensional electron gas

Designing a broad-spectrum gas sensor capable of identifying gas components in complex environments, such as mixed atmospheres or extreme temperatures, is a significant concern for various technologies, including energy, geological science, and planetary exploration. The main challenge lies in finding materials that exhibit high chemical stability and wide working temperature range. Materials that amplify signals through non-chemical methods could open up new sensing avenues. Here, we present the discovery of a broad-spectrum gas sensor utilizing correlated two-dimensional electron gas at a delta-doped LaAlO3/SrTiO3 interface with LaFeO3. Our study reveals that a back-gating on this two-dimensional electron gas can induce a non-volatile metal to insulator transition, which consequently can activate the two-dimensional electron gas to sensitively and quantitatively probe very broad gas species, no matter whether they are polar, non-polar, or inert gases. Different gas species cause resistance change at their sublimation or boiling temperature and a well-defined phase transition angle can quantitatively determine their partial pressures. Such unique correlated two-dimensional electron gas sensor is not affected by gas mixtures and maintains a wide operating temperature range. Furthermore, its readout is a simple measurement of electric resistance change, thus providing a very low-cost and high-efficient broad-spectrum sensing technique.</p