Background Genetic studies have implicated rare and common variations in liability for autism spectrum disorder (ASD). Of the discovered risk variants, those rare in the population invariably have large impact on liability, while common variants have small effects. Yet, collectively, common risk variants account for the majority of population-level variability. How these rare and common risk variants jointly affect liability for individuals requires further study. Methods To explore how common and rare variants jointly affect liability, we assessed two cohorts of ASD families characterized for rare and common genetic variations (Simons Simplex Collection and Population-Based Autism Genetics and Environment Study). We analyzed data from 3011 affected subjects, as well as two cohorts of unaffected individuals characterized for common genetic variation: 3011 subjects matched for ancestry to ASD subjects and 11,950 subjects for estimating allele frequencies. We used genetic scores, which assessed the relative burden of common genetic variation affecting risk of ASD (henceforth “burden”), and determined how this burden was distributed among three subpopulations: ASD subjects who carry a potentially damaging variant implicated in risk of ASD (“PDV carriers”); ASD subjects who do not (“non-carriers”); and unaffected subjects who are assumed to be non-carriers. Results Burden harbored by ASD subjects is stochastically greater than that harbored by control subjects. For PDV carriers, their average burden is intermediate between non-carrier ASD and control subjects. Both carrier and non-carrier ASD subjects have greater burden, on average, than control subjects. The effects of common and rare variants likely combine additively to determine individual-level liability. Limitations Only 305 ASD subjects were known PDV carriers. This relatively small subpopulation limits this study to characterizing general patterns of burden, as opposed to effects of specific PDVs or genes. Also, a small fraction of subjects that are categorized as non-carriers could be PDV carriers. Conclusions Liability arising from common and rare risk variations likely combines additively to determine risk of any individual diagnosed with ASD. On average, ASD subjects carry a substantial burden of common risk variation, even if they also carry a rare PDV affecting risk.

Two-dimensional (2D) rare-earth oxides (REO) are a large family of materials with various intriguing applications and the precise facet control is essential for investigating new properties in the 2D limit. However, a bottleneck remains for obtaining their 2D single crystals with specific facets because of the intrinsic non-layered structure and disparate thermodynamic stability of different facets. Herein, for the first time, we achieved the synthesis of a wide variety of high-quality 2D REO single crystals with tailorable facets via designing a hard-soft-acid-base (HSAB) couple for controlling the 2D nucleation of the predetermined facets and adjusting the growth mode and direction of crystals. Also, the facet-related magnetic properties of 2D REO single crystals were revealed. Our approach provides a foundation for further exploring other facet-dependent properties and various applications of 2D REO and an inspiration for the precise growth of other non-layered 2D materials as well.

In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly improve upon those of standard multi-armed bandit (MAB) algorithms under mild conditions. Lastly, we prove our mild conditions are necessary: without them one cannot do better than standard MAB bandit algorithms.

In a low-rank linear bandit problem, the reward of an action (represented by a matrix of size d1 × d2) is the inner product between the action and an unknown low-rank matrix Θ * . We propose an algorithm based on a novel combination of online-to-confidence-set conversion (Abbasi-Yadkori et al., 2012) and the exponentially weighted average forecaster constructed by a covering of low-rank matrices. In T rounds, our algorithm achieves O((d1 + d2) 3/2 √ rT ) regret that improves upon the standard linear bandit regret bound of O(d1d2 √ T ) when the rank of Θ * : r min{d1, d2}. We also extend our algorithmic approach to the generalized linear setting to get an algorithm which enjoys a similar bound under regularity conditions on the link function. To get around the computational intractability of covering based approaches, we propose an efficient algorithm by extending the "Explore-Subspace-Then-Refine" algorithm of Jun et al. (2019). Our efficient algorithm achieves O((d1 + d2) 3/2 √ rT ) regret under a mild condition on the action set X and the r-th singular value of Θ * . Our upper bounds match the conjectured lower bound of Jun et al. ( 2019) for a subclass of low-rank linear bandit problems. Further, we show that existing lower bounds for the sparse linear bandit problem strongly suggest that our regret bounds are unimprovable. To complement our theoretical contributions, we also conduct experiments to demonstrate that our algorithm can greatly outperform the performance of the standard linear bandit approach when Θ * is low-rank.

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