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Non-Hermitian systems hosting exceptional points (EPs) exhibit signal enhancement and unconventional mode dynamics. Going beyond isolated EPs, here we report on the existence of exceptional rings (ERs) in planar optical resonators with a specific form of circular dichroism and TE–TM splitting. Such exceptional rings possess intriguing topologies as discussed earlier for condensed matter systems, but they remain virtually unexplored in the presence of nonlinearity, for which our photonic platform is ideal. We find that when Kerr-type nonlinearity (or saturable gain) is introduced, the linear ER splits into two concentric ERs, with the larger-radius ring being a ring of third-order EPs. Transitioning from linear to nonlinear regime, we present a rigorous analysis of (spectral and band) topologies and report an enhanced and adjustable perturbation response in the nonlinear regime. Whereas certain features are specific to our system, the results on non-Hermitian topologies and nonlinearity-enhanced perturbation responses are generic and equally relevant to a broad class of other nonlinear non-Hermitian systems, providing a universal framework for engineering ERs and EPs in nonlinear non-Hermitian systems.
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The NAEP EDM Competition: On the Value of Theory-Driven Psychometrics and Machine Learning for Predictions Based on Log Data
The 2nd Annual WPI-UMASS-UPENN EDM Data Min- ing Challenge required contestants to predict efficient test taking based on log data. In this paper, we describe our theory-driven and psychometric modeling approach. For feature engineering, we employed the Log-Normal Response Time Model for estimating latent person speed, and the Generalized Partial Credit Model for estimating latent person ability. Additionally, we adopted an n-gram feature approach for event sequences. For training a multi-label classifier, we distinguished inefficent test takers who were going too fast and those who were going too slow, instead of using the provided binary target label. Our best-performing ensemble classify er comprised three sets of low-dimensional classi ers, dominated by test-taker speed. While our classi- er reached moderate performance, relative to competition leaderboard, our approach makes two important contributions. First, we show how explainable classi ers could provide meaningful predictions if results can be contextualized to test administrators who wish to intervene or take action. Second, our re-engineering of test scores enabled us to incorporate person ability into the estimation. However, ability was hardly predictive of efficient behavior, leading to the conclusion that the target label's validity needs to be questioned. The paper concludes with tools that are helpful for substantively meaningful log data mining.
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- Award ID(s):
- 1636847
- PAR ID:
- 10190399
- Date Published:
- Journal Name:
- Educational Data Mining
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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