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Most existing diagnostic models are developed to detect whether students have mastered a set of skills of interest, but few have focused on identifying what scientific misconceptions students possess. This article developed a general dual‐purpose model for simultaneously estimating students' overall ability and the presence and absence of misconceptions. The expectation‐maximization algorithm was developed to estimate the model parameters. A simulation study was conducted to evaluate to what extent the parameters can be accurately recovered under varied conditions. A set of real data in science education was also analyzed to examine the viability of the proposed model in practice.

In this work, we present a reproducible suite of test problems for large-scale optimization (“inverse design” and “topology optimization”) in photonics, where the prevalence of irregular, non-intuitive geometries can otherwise make it challenging to be confident that new algorithms and software are functioning as claimed. We include test problems that exercise a wide array of physical and mathematical features—far-field metalenses, 2d and 3d mode converters, resonant emission and focusing, and dispersion/eigenvalue engineering—and introduce ana posteriorilengthscale metric for comparing designs produced by disparate algorithms. For each problem, we incorporate cross-checks against multiple independent software packages and algorithms, and reproducible designs and their validations scripts are included. We believe that this suite should make it much easier to develop, validate, and gain trust in future inverse-design approaches and software.

In this article, a testlet hierarchical diagnostic classification model (TH-DCM) was introduced to take both attribute hierarchies and item bundles into account. The expectation-maximization algorithm with an analytic dimension reduction technique was used for parameter estimation. A simulation study was conducted to assess the parameter recovery of the proposed model under varied conditions, and to compare TH-DCM with testlet higher-order CDM (THO-DCM; Hansen, M. (2013). Hierarchical item response models for cognitive diagnosis (Unpublished doctoral dissertation). UCLA; Zhan, P., Li, X., Wang, W.-C., Bian, Y., & Wang, L. (2015). The multidimensional testlet-effect cognitive diagnostic models. Acta Psychologica Sinica, 47(5), 689. https://doi.org/10.3724/SP.J.1041.2015.00689 ). Results showed that (1) ignoring large testlet effects worsened parameter recovery, (2) DCMs assuming equal testlet effects within each testlet performed as well as the testlet model assuming unequal testlet effects under most conditions, (3) misspecifications in joint attribute distribution had an differential impact on parameter recovery, and (4) THO-DCM seems to be a robust alternative to TH-DCM under some hierarchical structures. A set of real data was also analyzed for illustration.

Meta‐optics have rapidly become a major research field within the optics and photonics community, strongly driven by the seemingly limitless opportunities made possible by controlling optical wavefronts through interaction with arrays of sub‐wavelength scatterers. As more and more modalities are explored, the design strategies to achieve desired functionalities become increasingly demanding, necessitating more advanced design techniques. Herein, the inverse design approach is utilized to create a set of single‐layer meta‐optics that simultaneously focus light and shape the spectra of focused light without using any filters. Thus, both spatial and spectral properties of the meta‐optics are optimized, resulting in spectra that mimic the color matching functions of the CIE 1931 XYZ color space, which links the spectral distribution of a light source to the color perception of a human eye. Experimental demonstrations of these meta‐optics show qualitative agreement with the theoretical predictions and help elucidate the focusing mechanism of these devices.