On the Performance of Semi- and Nonparametric Item Response Functions in Computer Adaptive Tests

Large-scale assessments often use a computer adaptive test (CAT) for selection of items and for scoring respondents. Such tests often assume a parametric form for the relationship between item responses and the underlying construct. Although semi- and nonparametric response functions could be used, there is scant research on their performance in a CAT. In this work, we compare parametric response functions versus those estimated using kernel smoothing and a logistic function of a monotonic polynomial. Monotonic polynomial items can be used with traditional CAT item selection algorithms that use analytical derivatives. We compared these approaches in CAT simulations with a variety of item selection algorithms. Our simulations also varied the features of the calibration and item pool: sample size, the presence of missing data, and the percentage of nonstandard items. In general, the results support the use of semi- and nonparametric item response functions in a CAT.

On sensitivity analysis of unsteady responses for FEM models of beams

This paper discusses optimal design of structures in terms of various quality criteria with limitations for the parameters of dynamic stress-strain state (steady, unsteady, spectral). Efficiency of the methods based on the compliance with indirect optimality criteria, in particular, on the Kuhn-Tucker conditions, considerably depends on fast and accurate calculations of derivatives for the parameters of state in terms of design parameters, which is achieved by obtaining the analytical expressions. Introduction of these expressions to the optimization of FEM-based models is only possible if structural design parameters and the parameters of stiffness matrix and element masses are linked explicitly. The purpose of this work is to finalize and verify the methods for obtaining analytical derivatives of design parameters as functions of vibration frequencies, forced harmonic vibration frequencies and natural vibration frequencies of finite-element model with subsequent transition to completely analytical (not subtractive) differentiation of unsteady and spectral responses of design parameters. For an FE model of beam with a large number (one hundred) of finite elements, this study obtained and verified, for various boundary conditions and loading scenarios, the distributions of sensitivity coefficients for steady dynamic parameters in terms of design parameters, i.e. cross-sections of elements.

Analytical Derivatives of the Individual State Energies in Ensemble Density Functional Theory Method: II. Implementation on Graphical Processing Units (GPUs)

Conical intersections control excited state reactivity and thus elucidation and prediction of their shapes and locations is crucial for photochemistry. To locate these intersections one needs accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g. XMS-CASPT2) are computationally difficult for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn-Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units (GPUs). We demonstrate that our implementation gives the correct topography and energetics of conical intersections for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient – the observed scaling with molecular size is sub-quadratic, i.e. O(N^1.77). This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.

Analytical Derivatives of the Individual State Energies in Ensemble Density Functional Theory Method: II. Implementation on Graphical Processing Units (GPUs)

Conical intersections control excited state reactivity and thus elucidation and prediction of their shapes and locations is crucial for photochemistry. To locate these intersections one needs accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g. XMS-CASPT2) are computationally difficult for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn-Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units (GPUs). We demonstrate that our implementation gives the correct topography and energetics of conical intersections for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient – the observed scaling with molecular size is sub-quadratic, i.e. O(N^1.77). This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.