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We consider the question of Gaussian mean testing, a fundamental task in high-dimensional distribution testing and signal processing, subject to adversarial corruptions of the samples. We focus on the relative power of different adversaries, and show that, in contrast to the common wisdom in robust statistics, there exists a strict separation between adaptive adversaries (strong contamination) and oblivious ones (weak contamination) for this task. Specifically, we resolve both the information-theoretic and computational landscapes for robust mean testing. In the exponential-time setting, we establish the tight sample complexity of testing N(0,I) against N(αv,I), where ∥v∥2=1, with an ε-fraction of adversarial corruptions, to be Θ~(max(d√α2,dε3α4,min(d2/3ε2/3α8/3,dεα2))) while the complexity against adaptive adversaries is Θ~(max(d√α2,dε2α4)) which is strictly worse for a large range of vanishing ε,α. To the best of our knowledge, ours is the first separation in sample complexity between the strong and weak contamination models. In the polynomial-time setting, we close a gap in the literature by providing a polynomial-time algorithm against adaptive adversaries achieving the above sample complexity Θ~(max(d−−√/α2,dε2/α4)), and a low-degree lower bound (which complements an existing reduction from planted clique) suggesting that all efficient algorithms require this many samples, even in the oblivious-adversary setting. 

As evidence grows supporting the importance of non-cognitive factors in learning, computer-assisted learning platforms increasingly incorporate non-academic interventions to influence student learning and learning related-behaviors. Non-cognitive interventions often attempt to influence students’ mindset, motivation, or metacognitive reflection to impact learning behaviors and outcomes. In the current paper, we analyze data from five experiments, involving seven treatment conditions embedded in mastery-based learning activities hosted on a computer-assisted learning platform focused on middle school mathematics. Each treatment condition embodied a specific non-cognitive theoretical perspective. Over seven school years, 20,472 students participated in the experiments. We estimated the effects of each treatment condition on students’ response time, hint usage, likelihood of mastering knowledge components, learning efficiency, and post-tests performance. Our analyses reveal a mix of both positive and negative treatment effects on student learning behaviors and performance. Few interventions impacted learning as assessed by the post-tests. These findings highlight the difficulty in positively influencing student learning behaviors and outcomes using non-cognitive interventions. 

A very high‐spatial resolution (∼21–23 m pixel at 85 km altitude) OH airglow imager at the Andes Lidar Observatory at Cerro Pachón, Chile observed considerable ducted wave activity on the night of 29–30 October 2016. This instrument was collocated with a Na wind‐temperature lidar that provided data revealing the occurrence of strong ducts. A large field of view OH and greenline airglow imager showed waves present over a vertical extent consistent with the altitudes of the ducting features identified in the lidar profiles. While waves that appeared to be ducted were seen in all imagers throughout the observation interval, the wave train seen in the OH images at earlier times had a distinct leading nonsinusoidal phase followed by several, lower‐amplitude, more sinusoidal phases, suggesting a likely bore. The leading phase exhibited significant dissipation via small‐scale secondary instabilities suggesting vortex rings that progressed rapidly to smaller scales and turbulence (the latter not fully resolved) thereafter. The motions of these small‐scale features were consistent with their location in the duct at or below ∼83–84 km. Bore dissipation caused a momentum flux divergence and a local acceleration of the mean flow within the duct along the direction of the initial bore propagation. A number of these features are consistent with mesospheric bores observed or modeled in previous studies.

 

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects leading to distortion in the signals. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some follow-up analyses that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system by applying these analyses to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. These analyses cover the strong lensing, millilensing, and microlensing regimes. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations.

 

In a neuron network, synapses update individually using local information, allowing for entirely decentralized learning. In contrast, elements in an artificial neural network are typically updated simultaneously using a central processor. Here, we investigate the feasibility and effect of desynchronous learning in a recently introduced decentralized, physics-driven learning network. We show that desynchronizing the learning process does not degrade the performance for a variety of tasks in an idealized simulation. In experiment, desynchronization actually improves the performance by allowing the system to better explore the discretized state space of solutions. We draw an analogy between desynchronization and mini-batching in stochastic gradient descent and show that they have similar effects on the learning process. Desynchronizing the learning process establishes physics-driven learning networks as truly fully distributed learning machines, promoting better performance and scalability in deployment.