Consider an opaque medium that contains 3D particles. All particles are convex bodies of the same shape, but they vary in size. The particles are randomly positioned and oriented within the medium and cannot be observed directly. Taking a planar section of the medium we obtain a sample of observed 2D section profile areas of the intersected particles. In this paper, the distribution of interest is the underlying 3D particle size distribution for which an identifiability result is obtained. Moreover, a non-parametric estimator is proposed for this size distribution. The estimator is proven to be consistent and its performance is assessed in a simulation study.

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A retrospective observational study utilising cancer incidence data from a population-based registry investigated determinants affecting primary liver cancer survival in a southern Italian region with high hepatitis viral infection rates and obesity prevalence. Among 2687 patients diagnosed between 2006 and 2019 (65.3% male), a flexible hazard-based regression model revealed factors influencing 5-year survival rates. High deprivation levels [HR = 1.41 (95%CI = 1.15–1.76); p < 0.001], poor access to care [HR = 1.99 (95%IC = 1.70–2.35); p < 0.0001], age between 65 and 75 [HR = 1.48 (95%IC = 1.09–2.01); p < 0.05] or >75 [HR = 2.21 (95%CI = 1.62–3.01); p < 0.0001] and residing in non-urban areas [HR = 1.35 (95%CI = 1.08–1.69); p < 0.01] were associated with poorer survival estimates. While deprivation appeared to be a risk factor for primary liver cancer patients residing within the urban area, the geographic distance from specialised treatment centres emerged as a potential determinant of lower survival estimates for residents in the non-urban areas. After balancing the groups of easy and poor access to care using a propensity score approach, poor access to care and a lower socioeconomic status resulted in potentially having a negative impact on primary liver cancer survival, particularly among urban residents. We emphasise the need to interoperate cancer registries with other data sources and to deploy innovative digital solutions to improve cancer prevention.

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In various stereological problems ann-dimensional convex body is intersected with an(n−1)-dimensionalIsotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associatedwith the(n−1)-dimensional volume of such a random section is studied. This distribution is also knownas 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 continuouswith respect to Lebesgue measure. A Monte Carlo simulation scheme is proposed for approximating thecorresponding probability density functions.@en

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.

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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 enrollment 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 enrollment 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.

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Introduction: Breast implant-associated anaplastic large-cell lymphoma (BIA-ALCL) 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. Methods: A quantitative analysis was performed by two independent researchers on cases extracted from 52 primary studies (case report, case series, and systematic review) published until April 2022 and searched in PubMed, Scopus, and Google-Scholar databases using “Breast-Implant” AND/OR “Associated” AND/OR “Anaplastic-Large-Cell-Lymphoma”. The statistical significance was verified by Student’s t-test for continuous variables, while Fisher’s exact test was applied for qualitative variables. Cox model with time-dependent covariates was used to estimate BIA-ALCL’s onset time. The Kaplan–Meier model allowed the estimation of the probability of survival after therapy according to breast implant exposure time. Results: Overall, 232 patients with BIA-ALCL were extracted. The mean age at diagnosis was 55 years old, with a mean time to disease onset from the first implant of 10.3 years. The hazard of developing BIA-ALCL in a shorter time resulted significantly higher for patients not having an implant replacement (hazard ratio = 0.03; 95%CI: 0.005–0.19; p-value < 0.01). Patients with implant replacement were significantly older than patients without previous replacement at diagnosis, having a median time to diagnosis since the first implant of 13 years (7 years in patients without replacement); anyway, the median time to BIA-ALCL occurrence since the last implantation was equal to 5 years. Discussion: Our findings suggest that, in BIA-ALCL patients, the implant substitution and/or capsulectomy may delay the disease’s onset. However, the risk of reoccurrence in an earlier time should be considered in these patients. Moreover, the time to BIA-ALCL onset slightly increased with age. Selection bias, lack of awareness, misdiagnosis, and limited data availability could be identified as limits of our study. An implant replacement should be considered according to a risk stratification approach to delay the BIA-ALCL occurrence in asymptomatic patients, although a stricter follow-up after the implant substitution should be recommended. Systematic Review Registration: https://www.crd.york.ac.uk/PROSPERO, identifier: CRD42023446726.

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Students’ and graduates’ mobility is an interesting topic of discussion especially for the Italian education system and universities. The main reasons for migration and for the so called brain drain, can be found in the socio-economic context and in the famous North–South divide. Measuring mobility and understanding its dynamic over time and space are not trivial tasks. Most of the studies in the related literature focus on the determinants of such phenomenon, in this paper, instead, combining tools coming from graph theory and Topological Data Analysis we propose a new measure for the attitude to mobility. Each mobility trajectory is represented by a graph and the importance of the features constituting the graph are evaluated over time using persistence diagrams. The attitude to mobility of the students is then ranked computing the distance between the individual persistence diagram and the theoretical persistence diagram of the stayer student. The new approach is used for evaluating the mobility of the students that in 2008 enrolled in an Italian university. The relation between attitude to mobility and the main socio-demographic variables is investigated.

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This study proposes a new approach to determine phenomenological or physical relations between microstructure features and the mechanical behavior of metals bridging advanced statistics and materials science in a study of the effect of hard precipitates on the hardening of metal alloys. Synthetic microstructures were created using multi-level Voronoi diagrams in order to control microstructure variability and then were used as samples for virtual tensile tests in a full-field crystal plasticity solver. A data-driven model based on Functional Principal Component Analysis (FPCA) was confronted with the classical Voce law for the description of uniaxial tensile curves of synthetic AISI 420 steel microstructures consisting of a ferritic matrix and increasing volume fractions of M23C6 carbides. The parameters of the two models were interpreted in terms of carbide volume fractions and texture using linear mixed-effects models. @en

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

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Abstract: The relationship between microstructure features and mechanical properties plays an important role in the design of materials and improvement of properties. Hole expansion capacity plays a fundamental role in defining the formability of metal sheets. Due to the complexity of the experimental procedure of testing hole expansion capacity, where many influencing factors contribute to the resulting values, the relationship between microstructure features and hole expansion capacity and the complexity of this relation is not yet fully understood. In the present study, an experimental dataset containing the phase constituents of 55 microstructures as well as corresponding properties, such as hole expansion capacity and yield strength, is collected from the literature. Statistical analysis of these data is conducted with the focus on hole expansion capacity in relation to individual phases, combinations of phases and number of phases. In addition, different machine learning methods contribute to the prediction of hole expansion capacity based on both phase fractions and chemical content. Deep learning gives the best prediction accuracy of hole expansion capacity based on phase fractions and chemical composition. Meanwhile, the influence of different microstructure features on hole expansion capacity is revealed. Graphical abstract: [Figure not available: see fulltext.]

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Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single-phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.

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Understanding the local strain enhancement and lattice distortion resulting from different microstructure features in metal alloys is crucial in many engineering processes. The development of heterogeneous strain not only plays an important role in the work hardening of the material but also in other processes such as recrystallization and damage inheritance and fracture. Isolating the contribution of precipitates to the development of heterogeneous strain can be challenging due to the presence of grain boundaries or other microstructure features that might cause ambiguous interpretation. In this work a statistical analysis of local strains measured by electron back scatter diffraction and crystal plasticity based simulations are combined to determine the effect of M₂₃C₆ carbides on the deformation of an annealed AISI 420 steel. Results suggest that carbides provide a more effective hardening at low plastic strain by a predominant long-range interaction mechanism than that of a pure ferritic microstructure. Carbides not only influence local strain directly by elastic incompatibilities with the ferritic matrix, but also the spatial interactions between ferrite grains. Carbides placed at the grain boundaries enhanced the development of strain near ferrite grain boundaries. However the positive effect of carbides and grain boundaries to develop high local strains is mitigated at regions with high density of carbides and ferrite grain boundaries.

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Understanding the relationship between microstructure features and mechanical properties is of great significance for the improvement and specific adjustment of steel properties. The relationship between mean grain size and yield strength is established by the well-known Hall-Petch equation. But due to the complexity of the grain configuration within materials, considering only the mean value is unlikely to give a complete representation of the mechanical behavior. The classical Taylor equation is often used to account for the effect of dislocation density, but not thoroughly tested in combination with grain size influence. In the present study, systematic heat treatment routes and cold rolling followed by annealing are designed for interstitial free (IF) steel to achieve ferritic microstructures that not only vary in mean grain size, but also in grain size distribution and in dislocation density, a combination that is rarely studied in the literature. Optical microscopy is applied to determine the grain size distribution. The dislocation density is determined through XRD measurements. The hardness is analyzed on its relation with the mean grain size, as well as with the grain size distribution and the dislocation density. With the help of the variable selection tool LASSO, it is shown that dislocation density, mean grain size and kurtosis of grain size distribution are the three features which most strongly affect hardness of IF steel.

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This thesis aims at the development of physical relations between the intricate 3D features of metallic microstructures and the mechanical properties of the material. For understanding which are the microstructural determinants of the resultingmechanical behaviour of metals, a deep quantitative characterisation of the microstructure is needed. The main steps of quantitative characterisation of the microstructures are: identification of the phases distribution and their chemical composition, study of the microstructure morphology (geometrical arrangement of grains, grain boundaries, grain orientations, grain size and grain shape). An accurate description of the microstructure features enriched with physical knowledge can lead to new insight into the relation between micro and macro properties. Advanced statistical tools are used to find relations between microstructural and mechanical quantities. Eventually, results coming from the statistical modelling of this relation will lead to the design of new materialswith desired properties.@en

Understanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for every value of the intensity parameter. Moreover, we use a sophisticated simulation program to construct a close Monte Carlo based approximation for the distributions of interest. Using this, we determine the closest approximating distributions within the mentioned frequently used parametric classes of distributions and conclude that these representations can be quite accurate. Finally we consider a 3D volume dataset and compare the real volume distribution to what is to be expected under the Poisson-Voronoi model.@en

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 influence most their occupational status and finally outlining a transition 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 University of Palermo among the different occupational states in three different times. We analyze data coming from a disproportionate stratified sample of graduates in 2009, interviewed three different times: one year (2010), three years (2012), five years (2014) after the graduation. 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 in- homogeneous multi-state Markov model with piecewise constant intensities; eventually implications from the main results are discussed.@en