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As a method to shorten the test time of the Force Concept Inventory (FCI), we suggest the use of computerized adaptive testing (CAT). CAT is the process of administering a test on a computer, with items (i.e., questions) selected based upon the responses of the examinee to prior items. In so doing, the test length can be significantly shortened. As a step to develop a CAT-based version of the FCI (FCI-CAT), we examined the optimal test length of the FCI-CAT such that accuracy and precision [which we measure in terms of bias, standard error, and root-mean-square error (RMSE)] of Cohen’s d would be comparable to that of the full FCI for a given class size. First, we estimated the item parameters of the FCI items based on the three-parameter logistic model of item response theory, which are used in the algorithm of CAT. For this estimation, we used 2882 responses of Japanese university students. Second, we conducted a Monte Carlo simulation to analyze how the bias, standard error, and RMSE of Cohen’s d depend upon the test length. Third, we conducted a post hoc simulation to examine the consistency of the Monte Carlo results with what would have been obtained using empirical responses. For this comparison, we used 86 pairs of pre- and post- test responses of Japanese university students. As a result, we found that for a class size of 40, we may reduce the test length of the FCI-CAT to 15–19 items, thereby reducing the test time of the FCI to 50%–63%, with an accompanying decrease in accuracy and precision of only 5%–10%. The results of the Monte Carlo study and the post hoc simulation were consistent, which supports the adequacy of our Monte Carlo study and its relevance in terms of administering the FCI-CAT in real classrooms.

In this study, we analyze the systematic error from false positives of the Force Concept Inventory (FCI). We compare the systematic errors of question 6 (Q.6), Q.7, and Q.16, for which clearly erroneous reasoning has been found, with Q.5, for which clearly erroneous reasoning has not been found. We determine whether or not a correct response to a given FCI question is a false positive using subquestions. In addition to the 30 original questions, subquestions were introduced for Q.5, Q.6, Q.7, and Q.16. This modified version of the FCI was administered to 1145 university students in Japan from 2015 to 2017. In this paper, we discuss our finding that the systematic errors of Q.6, Q.7, and Q.16 are much larger than that of Q.5 for students with mid-level FCI scores. Furthermore, we find that, averaged over the data sample, the sum of the false positives from Q.5, Q.6, Q.7, and Q.16 is about 10% of the FCI score of a midlevel student.

We propose a dynamic model for the economic growth (ΔG) and the diffusion index (DI) in order to explain the business cycle. This model is described by equations analogous to the optimal velocity model in traffic flow. In the model there exists a conserved quantity, which corresponds to the total energy in a dynamical system. We found that the business cycle with the period 5–8 years is favorably reproduced, since the model predicts a periodic motion in the conservative system.

We develop a systematic DLCQ perturbation theory and show that DLCQ S-matrix does not have a covariant continuum limit for processes with $p^+=0$ exchange. This implies that the role of the zero mode is more subtle than ever considered in DLCQ and hence must be treated with great care also in non-perturbative approach. We also make a brief comment on DLCQ in string theory., 4 pages, 2 figures

In this study, we evaluate the structural validity of Q.16 and Q.7 in the Force Concept Inventory (FCI). We address whether respondents who answer Q.16 and Q.7 correctly actually have an understanding of the concepts of physics tested in the questions. To examine respondents’ levels of understanding, we use subquestions that test them on concepts believed to be required to answer the actual FCI questions. Our sample size comprises 111 respondents; we derive false-positive ratios for prelearners and postlearners and then statistically test the difference between them. We find a difference at the 0.05 significance level for both Q.16 and Q.7, implying that it is possible for postlearners to answer both questions without an understanding of the concepts of physics tested in the questions; therefore, the structures of Q.16 and Q.7 are invalid. In this study, we only evaluate the validity of these two FCI questions; we do not assess the validity of previous studies that have compared total FCI scores.

The spectrum of the massive Schwinger model in the strong coupling region is obtained by using the light-front Tamm-Dancoff (LFTD) approximation up to including six-body states. We numerically confirm that the two-meson bound state has a negligibly small six-body component. Emphasis is on the usefulness of the information about states (wave functions). It is used for identifying the three-meson bound state among the states below the three-meson threshold. We also show that the two-meson bound state is well described by the wave function of the relative motion., 19 pages, RevTeX, 7 figures are available upon request; Minor errors have been corrected; Final version to appear in Phys.Rev.D

The massive Schwinger model with two flavors is studied in the strong coupling region by using the light-front Tamm-Dancoff approximation. The mass spectrum of the lightest particles is obtained numerically. We find that the mass of the lightest isotriplet ("pion") behaves as ${m}^{0.50}$ for strong coupling, where $m$ is the fermion mass. We also find that the lightest isosinglet is not in the valence state ("$\ensuremath{\eta}$") which is much heavier in the strong coupling region, but can be interpreted as a bound state of two pions. It is 1.762 times heavier than the pion at $m=1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}(\frac{e}{\sqrt{\ensuremath{\pi}}})$, while Coleman predicted that the ratio is \ensuremath{\surd}3 in the strong coupling limit. The "pion decay constant" is calculated to be 0.3945.

We study a (1+1)-dimensional $\lambda\phi^4$ model with a light-cone zero mode and constant external source to describe spontaneous symmetry breaking. In the broken phase, we find degenerate vacua and discuss their stability based on effective-potential analysis. The vacuum triviality is spurious in the broken phase because these states have lower energy than Fock vacuum. Our results are based on the variational principle., Comment: 4 pages, 2 figures, to appear in Phys. Rev. Lett

We study (1+1)-dimensional φ4 theory quantized on the light cone. We pay much attention to the light-front zero mode, and find the second-order phase transition in the strong coupling region by solving the zero-mode constraint with a new method. We also obtain the critical coupling constant, λc=24μR2, which is consistent with the equal-time calculations, and the critical exponent, β=1/2.

The massive Schwinger model is quantized on the light cone with great care on the bosonic zero modes by putting the system in a finite (light-cone) spatial box. The zero mode of $A_{-}$ survives Dirac's procedure for the constrained system as a dynamical degree of freedom. After regularization and quantization, we show that the physical space condition is consistently imposed and relates the fermion Fock states to the zero mode of the gauge field. The vacuum is obtained by solving a Schr\"odinger equation in a periodic potential, so that the theta is understood as the Bloch momentum. We also construct a one-meson state in the fermion-antifermion sector and obtained the Schr\"odinger equation for it., Comment: 23 pages, RevTex, no figures

We investigate mesons in the bosonized massive Schwinger model in the light-front Tamm-Dancoff approximation in the strong coupling region. We confirm that the three-meson bound state has a few percent fermion six-body component in the strong coupling region when expressed in terms of fermion variables, consistent with our previous calculations. We also discuss some qualitative features of the three-meson bound state based on the information about the wave function., 19 pages, RevTex, included 6 figures which are compressed and uuencoded