Constraints on the Reheating Parameters after Gauss-Bonnet Inflation from the Primordial Gravitational Waves

We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.Comment: 27 pages, 8 figures, v2: matches the published versio

The Use of Rasch Model to Create Adaptive Practices in e-Learning Systems

While different approaches were developed to create computerized adaptive practices for e-learning systems, we show that exploiting Rasch models to create adaptive practices can be a new promising approach. Rasch analysis enables us to find a mathematical model to analyze students’ answers to exam questions by representing students’ abilities and questions difficulty levels on the same scale. In this paper, we introduce a novel algorithm to generate adaptive practices based on the Rasch analysis of students’ performance in an initial assessment. This approach enables us to generate adaptive practices that consider not only the student’s ability and his previous performance but also the difficulty level of each question. We also present results from a preliminary field experiment that we have conducted using an online learning system that implements this algorithm. The potential advantages of this approach and the practical contributions are discussed