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Previous work has shown that item response theory may be used to rank incorrect response options to multiple-choice items on commonly used assessments. This work has shown that, when the correct response to each item is specified, a nominal response model (NRM) may be used to rank the incorrect options. We seek to determine the robustness of these results by applying the NRM to all response choices, without specifying the correct response. We apply these analyses to multiple data sets (each with more than 9,000 response sets), including pre-instruction and post-instruction responses. We find that the rankings generated without specifying the correct response are consistent with the previously published rankings for one data set; however, we find noticeable differences between rankings generated from different data sets. We provide evidence that discrepancies may result from differences in response rates for less commonly chosen responses.

The paper focuses on identifying the causes of student performance to provide personalized recommendations for improving pass rates. We introduce the need to move beyond predictive models and instead identify causal relationships. We propose using causal discovery techniques to achieve this. The study's main contributions include using causal discovery to identify causal predictors of student performance and applying counterfactual analysis to provide personalized recommendations. The paper describes the application of causal discovery methods, specifically the PC algorithm, to real-life student performance data. It addresses challenges such as sample size limitations and emphasizes the role of domain knowledge in causal discovery. The results reveal the identified causal relationships, such as the influence of earlier test grades and mathematical ability on final student performance. Limitations of this study include the reliance on domain expertise for accurate causal discovery, and the necessity of larger sample sizes for reliable results. The potential for incorrect causal structure estimations is acknowledged. A major challenge remains, which is the real-time implementation and validation of counterfactual recommendations. In conclusion, the paper demonstrates the value of causal discovery for understanding student performance and providing personalized recommendations. It highlights the challenges, benefits, and limitations of using causal inference in an educational context, setting the stage for future studies to further explore and refine these methods., Comment: 11 pages

Counterfactual explanations (CEs) are methods for generating an alternative scenario that produces a different desirable outcome. For example, if a student is predicted to fail a course, then counterfactual explanations can provide the student with alternate ways so that they would be predicted to pass. The applications are many. However, CEs are currently generated from machine learning models that do not necessarily take into account the true causal structure in the data. By doing this, bias can be introduced into the CE quantities. I propose in this study to test the CEs using Judea Pearl's method of computing counterfactuals which has thus far, surprisingly, not been seen in the counterfactual explanation (CE) literature. I furthermore evaluate these CEs on three different causal structures to show how the true underlying causal structure affects the CEs that are generated. This study presented a method of evaluating CEs using Pearl's method and it showed, (although using a limited sample size), that thirty percent of the CEs conflicted with those computed by Pearl's method. This shows that we cannot simply trust CEs and it is vital for us to know the true causal structure before we blindly compute counterfactuals using the original machine learning model.

We demonstrate an axisymmetric inverse-designed metalens to improve the performance of zone-plate-array lithography (ZPAL), one of the maskless lithography approaches, that offer a new paradigm for nanoscale research and industry. First, we derive a computational upper bound for a unit-cell-based axisymmetric metalens. Then, we demonstrate a fabrication-compatible inverse-designed metalens with 85.50\% transmission normalized focusing efficiency at 0.6 numerical aperture at 405nm wavelength; a higher efficiency than a theoretical gradient index lens design (79.98\%). We also demonstrate experimental validation for our axisymmetric inverse-designed metalens via electron beam lithography. Metalens-based maskless lithography may open a new way of achieving low-cost, large-area nanofabrication.

Measuring treatment effects in observational studies is challenging because of confounding bias. Confounding occurs when a variable affects both the treatment and the outcome. Traditional methods such as propensity score matching estimate treatment effects by conditioning on the confounders. Recent literature has presented new methods that use machine learning to predict the counterfactuals in observational studies which then allow for estimating treatment effects. These studies however, have been applied to real world data where the true treatment effects have not been known. This study aimed to study the effectiveness of this counterfactual prediction method by simulating two main scenarios: with and without confounding. Each type also included linear and non-linear relationships between input and output data. The key item in the simulations was that we generated known true causal effects. Linear regression, lasso regression and random forest models were used to predict the counterfactuals and treatment effects. These were compared these with the true treatment effect as well as a naive treatment effect. The results show that the most important factor in whether this machine learning method performs well, is the degree of non-linearity in the data. Surprisingly, for both non-confounding \textit{and} confounding, the machine learning models all performed well on the linear dataset. However, when non-linearity was introduced, the models performed very poorly. Therefore under the conditions of this simulation study, the machine learning method performs well under conditions of linearity, even if confounding is present, but at this stage should not be trusted when non-linearity is introduced.

We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These compound objects can be tuned smoothly from having a concave to a convex surface. We show that even two of these composite particles can exhibit collective motion modifying the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behaviour of many such particles.

We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting liquid and crystal phases. Measurements of the orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-crystal one. The interplay of boundary inelasticity and geometry, either order-promoting or inhibiting, controls the wetting of the granular crystal / fluid. This order induced wetting has important consequences, determining how coexisting phases separate spatially.

We use a symmetry-motivated approach to analyse neutron pair distribution function data to investigate the mechanism of negative thermal expansion (NTE) in ReO$_3$. This analysis shows that the local structure of ReO$_3$ is dominated by an in-phase octahedral tilting mode and that the octahedral units are far less flexible to scissoring type deformations than the octahedra in the related compound ScF$_3$. These results support the idea that structural flexibility is an important factor in NTE materials, allowing the phonon modes that drive a volume contraction of the lattice to occupy a greater volume in reciprocal space. The lack of flexibility in ReO$_3$ restricts the NTE-driving phonons to a smaller region of reciprocal space, limiting the magnitude and temperature range of NTE. In addition, we investigate the thermal expansion properties of the material at high temperature and do not find the reported second NTE region. Finally, we show that the local fluctuations, even at elevated temperatures, respect the symmetry and order parameter direction of the observed $P4/mbm$ high pressure phase of ReO$_3$. The result indicates that the motions associated with rigid unit modes are highly anisotropic in these systems., Comment: 9 pages, 6 figures

We report a systematic study of the $5d$-electron-doped system Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($0 \leq x \leq 0.15$). With increasing $x$, the orthorhombic $b$~axis decreases slightly while accompanying changes in $a$ and $c$ leave the unit cell volume almost unchanged. Inelastic neutron scattering, along with thermal and transport measurements, reveal that for the Kondo semiconductor CeFe$_2$Al$_{10}$, the low-temperature energy gap which is proposed to be a consequence of strong $c \mhyphen f$ hybridization, is suppressed by a small amount of Ir substitution for Fe, and that the system adopts a metallic ground state with an increase in the density of states at the Fermi level. The charge or transport gap collapses (at $x=$~0.04) faster than the spin gap with Ir substitution. Magnetic susceptibility, heat capacity, and muon spin relaxation measurements demonstrate that the system undergoes long-range antiferromagnetic order below a N\'eel temperature, $T_{\mathrm{N}}$, of 3.1(2)~K for $x = 0.15$. The ordered moment is estimated to be smaller than 0.07(1)~$\mu_\mathrm{B}$/Ce although the trivalent state of Ce is confirmed by Ce L$_3$-edge x-ray absorption near edge spectroscopy. It is suggested that the $c \mhyphen f$ hybridization gap, which plays an important role in the unusually high ordering temperatures observed in Ce$T_2$Al$_{10}$ ($T$ = Ru and Os), may not be necessary for the onset of magnetic order with a low $T_{\mathrm{N}}$ seen here in Ce(Fe$_{1-x}$Ir$_x$)$_2$Al$_{10}$., Comment: 12 pages, 11 figures

Ishimoto, Davenport, and Wittmann have previously reported analyses of data from student responses to the Force and Motion Conceptual Evaluation (FMCE), in which they used item response curves (IRCs) to make claims about American and Japanese students' relative likelihood to choose certain incorrect responses to some questions. We have used an independent data set of over 6,500 American students' responses to the FMCE to generate IRCs to test their claims. Converting the IRCs to vectors, we used dot product analysis to compare each response item quantitatively. For most questions, our analyses are consistent with Ishimoto, Davenport, and Wittmann, with some results suggesting more minor differences between American and Japanese students than previously reported. We also highlight the pedagogical advantages of using IRCs to determine the differences in response patterns for different populations to better understand student thinking prior to instruction.

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either understanding of physics concepts or problem-solving abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL) as a tool for measuring quantitative literacy, a foundation of mathematical reasoning, in the context of introductory physics. We present the development of the PIQL and evidence of its validity for use in calculus-based introductory physics courses. Unlike concept inventories, the PIQL is a reasoning inventory, and can be used to assess reasoning over the span of students' instruction in introductory physics. Although mathematical reasoning associated with the PIQL is taught in prior mathematics courses, pre/post test scores reveal that this reasoning isn't readily used by most students in physics, nor does it develop as part of physics instruction--even in courses that use high-quality, research-based curricular materials. As has been the case with many inventories in physics education, we expect use of the PIQL to support the development of instructional strategies and materials--in this case, designed to meet the course objective that all students become quantitatively literate in introductory physics.

We have developed the Physics Inventory of Quantitative Literacy (PIQL) as a tool to measure students' quantitative literacy in the context of introductory physics topics. We present the results from various quantitative analyses used to establish the validity of both the individual items and the PIQL as a whole. We show how examining the results from classical test theory analyses, factor analysis, and item response curves informed decisions regarding the inclusion, removal, or modification of items. We also discuss how the choice to include multiple-choice/multiple-response items has informed both our choices for analyses and the interpretations of their results. We are confident that the most recent version of the PIQL is a valid and reliable instrument for measuring students' physics quantitative literacy in calculus-based introductory physics courses at our primary research site. More data are needed to establish its validity for use at other institutions and in other courses., Comment: accepted for publication: 2020 Physics Education Research Conference

We present a structural and magnetic study on two batches of polycrystalline LiNi$_{0.8}$Mn$_{0.1}$Co$_{0.1}$O$_2$ (commonly known as Li NMC 811), a Ni-rich Li ion battery cathode material, using elemental analysis, X-ray and neutron diffraction, magnetometry, and polarised neutron scattering measurements. We find that the samples, labelled S1 and S2, have the composition Li$_{1-x}$Ni$_{0.9+x-y}$Mn$_y$Co$_{0.1}$O$_2$, with $x = 0.025(2)$, $y = 0.120(2)$ for S1 and $x = 0.002(2)$, $y = 0.094(2)$ for S2, corresponding to different concentrations of magnetic ions and excess Ni$^{2+}$ in the Li$^+$layers. Both samples show a peak in the zero-field cooled (ZFC) dc susceptibility at 8.0(2) K but the temperature at which the ZFC and FC (field-cooled) curves deviate is substantially different: 64(2) K for S1 and 122(2) K for S2. Ac susceptibility measurements show that the transition for S1 shifts with frequency whereas no such shift is observed for S2 within the resolution of our measurements. Our results demonstrate the sample dependence of magnetic properties in Li NMC 811, consistent with previous reports on the parent material LiNiO$_2$. We further establish that a combination of experimental techniques are necessary to accurately determine the chemical composition of next generation battery materials with multiple cations., Comment: Revised manuscript, 27 pages main text, 6 figures, 5 pages supplementary material. Accepted for publication in Inorganic Chemistry