Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

Gravitational self-localization for spherical masses

In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, M≲10−17 kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schrödinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes R≈10−7 m, and the density of the material causes only minor variations in this value.

Gli studi italiani sulla regina Cristina di Svezia negli ultimi cinquant'anni

Queen Christina of Sweden (1626-1689)) is probably the most important individual to directly link the cultures of Sweden and Italy, and thus fascinate scholars over the last four centuries. In the last fifty years, research on and interest in this monarch has been particularly intense. This has led to current international scientific debate concerning all the different cultural expressions in which Queen Cristina was particularly involved. However, until now there has been lacking a comprehensive work to illustrate the development of scientific research in Italian on Queen Christina. This article, therefore, without claiming to be exhaustive, aims to fill this gap by identifying the main direction of current research. The article, after briefly introducing previous works (both Italian and Swedish), demonstrates how the first major renaissance of international studies on Queen Cristina took place in Sweden in the early 1960s. Even more important was the subsequent turning point in 1989, when the tercentenary of the death of Queen Christina was celebrated and the Azzolino Collection at the Biblioteca Comunale in Jesi was opened. The article focuses on the studies in Italian during this latter period. To make the exposition more organic and, importantly, more accessible to those readers interested in only one particular aspect of the scientific studies about Queen Christina, the studies in Italian since 1689 are divided into different subject areas.