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Cognitive Diagnosis Models in educational measurement are restricted latent class models that describe ability in a knowledge domain as a composite of latent skills an examinee may have mastered or failed. Different combinations of skills define distinct latent proficiency classes to which examinees are assigned based on test performance. Items of cognitively diagnostic assessments are characterized by skill profiles specifying which skills are required for a correct item response. The item-skill profiles of a test form its Q-matrix. The validity of cognitive diagnosis depends crucially on the correct specification of the Q-matrix. Typically, Q-matrices are determined by curricular experts. However, expert judgment is fallible. Data-driven estimation methods have been developed with the promise of greater accuracy in identifying the Q-matrix of a test. Yet, many of the extant methods encounter computational feasibility issues either in the form of excessive amounts of CPU times or inadmissible estimates. In this article, a two-step algorithm for estimating the Q-matrix is proposed that can be used with any cognitive diagnosis model. Simulations showed that the new method outperformed extant estimation algorithms and was computationally more efficient. It was also applied to Tatsuoka’s famous fraction-subtraction data. The paper concludes with a discussion of theoretical and practical implications of the findings.

 

Realizing nonlinear interactions between spatially separated particles can advance molecular science and technology, including remote catalysis of chemical reactions, ultrafast processing of information in infrared (IR) photonic circuitry, and advanced platforms for quantum simulations with increased complexity. Here, we achieved nonlinear interactions at ultrafast time scale between polaritons contained in spatially adjacent cavities in the mid-IR regime, altering polaritons in one cavity by pumping polaritons in an adjacent one. This was done by strong coupling molecular vibrational modes with photon modes, a process that combines characteristics of both photon delocalization and molecular nonlinearity. The dual photon/molecule character of polaritons enables delocalized nonlinearity—a property that neither molecular nor cavity mode would have alone. 

Using a combination of two-dimensional infrared (2D IR) and variable temperature Fourier transform infrared (FTIR) spectroscopies the rapid structural isomerization of a five-coordinate ruthenium complex is investigated. In methylene chloride, three exchanging isomers were observed: (1) square pyramidal equatorial, ( 1 ); (2) trigonal bipyramidal, ( 0 ); and (3) square pyramidal apical, ( 2 ). Exchange between 1 and 0 was found to be an endergonic process (Δ H = 0.84 (0.08) kcal mol −1 , Δ S = 0.6 (0.4) eu) with an isomerization time constant of 4.3 (1.5) picoseconds (ps, 10 −12 s). Exchange between 0 and 2 however was found to be exergonic (Δ H = −2.18 (0.06) kcal mol −1 , Δ S = −5.3 (0.3) eu) and rate limiting with an isomerization time constant of 6.3 (1.6) ps. The trigonal bipyramidal complex was found to be an intermediate, with an activation barrier of 2.2 (0.2) kcal mol −1 and 2.4 (0.2) kcal mol −1 relative to the equatorial and apical square pyramidal isomers respectively. This study provides direct validation of the mechanism of Berry pseudorotation – the pairwise exchange of ligands in a five-coordinate complex – a process that was first described over fifty years ago. This study also clearly demonstrates that the rate of pseudorotation approaches the frequency of molecular vibrations. 

Selective vibrational energy transfer between molecules in the liquid phase, a difficult process hampered by weak intermolecular forces, is achieved through polaritons formed by strong coupling between cavity photon modes and donor and acceptor molecules. Using pump-probe and two-dimensional infrared spectroscopy, we found that the excitation of the upper polariton, which is composed mostly of donors, can efficiently relax to the acceptors within ~5 picoseconds. The energy-transfer efficiency can be further enhanced by increasing the cavity lifetime, suggesting that the energy transfer is a polaritonic process. This vibrational energy-transfer pathway opens doors for applications in remote chemistry, sensing mechanisms, and vibrational polariton condensation.