Topology-based goodness-of-fit tests for sliced spatial data

In materials science and many other application domains, 3D information can often only be obtained by extrapolating from 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. It is illustrated how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, goodness-of-fit tests that become asymptotically exact in large sampling windows are devised. The testing methodology is illustrated through a detailed simulation study and a prototypical example from materials science is provided

Existence and approximation of densities of chord length- and cross section area distributions

In various stereological problems an n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions

Existence and Approximation of Densities of Chord Length- and Cross Section Area Distributions

In various stereological problems a n-dimensional convex body is intersected with an (n−1)-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the (n−1)-dimensional volume of such a random section is studied. This distribution is also known as chord length distribution and cross section area distribution in the planar and spatial case respectively. For various classes of convex bodies it is shown that these distribution functions are absolutely continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating the corresponding probability density functions

Implant replacement and anaplastic large cell lymphoma associated with breast implants: a quantitative analysis

Breast implant-associated anaplastic large-cell lymphoma (BIAALCL) is a rare form of non-Hodgkin T-cell lymphoma associated with breast reconstruction post-mastectomy or cosmetic-additive mammoplasty. The increasing use of implants for cosmetic purposes is expected to lead to an increase in BIA-ALCL cases. This study investigated the main characteristics of the disease and the factors predicting BIA-ALCL onset in patients with and without an implant replacement

Does taking additional Maths classes improve university performance?

Several recent studies in educational literature showed how students’ skills in maths affect their success at higher levels of education. The aim of this paper is to evaluate the effect of taking additional maths class at high school on first-year performance of Italian university students. However, university performance and the choice of the high-school depend on several factors that make this evaluation challenging. Using information coming from three different sources, we carry out a multilevel propensity score procedure to estimate the average treatment effect between the applied sciences track and the traditional scientific one. After balancing for school- and student-level covariates, the results of a logistic regression model suggest no difference between the two school tracks

Does taking additional Maths classes in high school affect academic outcomes?

Several studies in the mathematical education literature show the effect of students’ high school skills in maths on their success at higher levels of education and work. In particular, the importance of maths course taking in US high schools is highlighted to be important for college enrolment and completion. The choice of taking additional maths courses or, as in Italy, of choosing a high-school curriculum with more maths, is not random: it depends on several substantial factors such as gender and socio-economic status. This selection bias implies that the differences in the academic outcomes might be traceable not only to mathematics ability and knowledge. In this paper, the aim is to estimate the treatment effect of attending a relatively new high school curriculum in Italy with more maths, with respect to the traditional track of the scientific “liceo”, on two academic outcomes: university enrolment and first-year university performance. After having reduced the selection bias using a caliper multi-level propensity score matching procedure, a multi-state Markov model is used to study the treatment effect on the joint educational outcomes

A longitudinal analysis of the occupational status of the graduates of the University of Palermo

The availability of a large amount of longitudinal data provided by the surveys carried out by STELLA (Statistics about Graduates and Labour Market) allowed us to describe the occupational paths of graduates of the University of Palermo. In this paper we refer to a disproportionate stratified sample of graduates in 2009, interviewed three dierent times: one year (2010), three years (2012), ve years (2014) after the graduation. In such a global economic crises context, our aims are describing the labour market of the Palermitan graduates, identifying the variables that influence most their occupational status and nally outlining a transition probability structure among the states: Work, Search for a Job, Study, Other. To achieve our aim, first we provide a brief descriptive analysis of the main characteristics of the graduates gathered by the three different surveys; secondly we fit a time inhomogeneous multi-state Markov model with piecewise constant intensities; eventually we try to give a measure of goodness of fit of the model, comparing the results with the observed frequencies

A mobility analysis of the occupational status of the graduates of the University of Palermo in an economic crisis context

In such a global economic crisis context, our aims are describing the mobil- ity of the Palermitan graduates in the labour market, identifying the variables that inuence most their occupational status and nally outlining a transi- tion probability structure among the states: Work, Search for a Job, Study, Other. The availability of a large amount of longitudinal data provided by the surveys carried out by STELLA (Statistics about Graduates and Labour Market) allowed us to analyze the mobility of the graduates of the Univer- sity of Palermo among the dierent occupational states in three dierent times. We analyze data coming from a disproportionate stratied sample of graduates in 2009, interviewed three dierent times: one year (2010), three years (2012), ve years (2014) after the graduation. To achieve our aim, rst we provide a brief descriptive analysis of the main characteristics of the graduates gathered by the three dierent surveys; secondly we t a time in- homogeneous multi-state Markov model with piecewise constant intensities; eventually implications from the main results are discussed.