Statistical Methodologies of Functional Data Analysis for Industrial Applications

This thesis stands as one of the first attempt to connect the statistical object oriented data analysis (OODA) methodologies with the industry field. Indeed, the aim of this thesis is to develop statistical methods to tackle industrial problems through the paradigm of the OODA. The new framework of Industry 4.0 requires factories that are equipped with sensor and advanced acquisition systems that acquire data with a high degree of complexity. OODA can be particularly suitable to deal with this increasing complexity as it considers each statistical unit as an atom or a data object assumed to be a point in a well-defined mathematical space. This idea allows one to deal with complex data structure by changing the resolution of the analysis. Indeed, from standard methods where the atom is represented by vector of numbers, the focus now is on methodologies where the objects of the analysis are whole complex objects. In particular, this thesis focuses on functional data analysis (FDA), a branch of OODA that considers as the atom of the analysis functions defined on compact domains. The cross-fertilization of FDA methods to industrial applications is developed into three parts in this dissertation. The first part presents methodologies developed to solve specific applicative problems. In particular, a first consistent portion of this part is focused on \textit{profile monitoring} methods applied to ship CO\textsubscript{2} emissions. A second portion deals with the problem of predicting the mechanical properties of an additively manufactured artifact given the particle size distribution of the powder used for its production. And, a third portion copes with the cluster analysis for the quality assessment of metal sheet spot welds in the automotive industry based on observations of dynamic resistance curve. Stimulated by these challenges, the second part of this dissertation turns towards a more methodological line that addresses the notion of \textit{interpretability} for functional data. In particular, two new interpretable estimators of the coefficient function of the function-on-function linear regression model are proposed, which are named S-LASSO and AdaSS, respectively. Moreover, a new method, referred to as SaS-Funclust, is presented for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. In the last part, two ongoing researches on FDA methods for industrial application are presented. In particular, the first one regards the definition of a new robust nonparametric functional ANOVA method (Ro-FANOVA) to test differences among group functional means by being robust against the presence of outliers with an application to additive manufacturing. The second one sketches a new methodological framework for the real-time profile monitoring

Serving through Transcribing: Preserving History while Building Community

Community is a foundational element in honors education. During the global pandemic, students reimagined ways to connect in order to build community and serve one another. Authors describe a virtual collaboration in transcription, where honors students gathered to participate in digital transcribe-a-thons. These informal groupings evolved into a transcribing club that met three times a week (collectively logging more than 1,600 hours) and transcribed over 16,000 historical documents. A study of participating transcribers reveals enhanced historical knowledge, skill building, and opportunities for relationships with students of varying interests and backgrounds despite edicts for social distancing. While a common feature of the club is a connection to something beyond the student, authors maintain that the experience of transcribing also brings a sense of connectedness with fellow honors students and the honors college. Authors provide student insight and outcomes as well as detailed instructions for honors practitioners seeking to introduce historical transcription to their students

Uptake and translocation of 134Cs by maize roots as affected by heterogeneous distribution of 134Cs

Structure-induced non-uniform water flow induces a heterogeneous distribution of surface-applied radionuclides in the soil profile. This study was conducted to assess the amount of 134Cs which can be taken up by a single root growing in an area enriched in 134Cs relative to the total amount of 134Cs that can be taken up by the whole root system growing in an area homogeneously contaminated with 134Cs. A split-root experiment was used to simulate the heterogeneous distribution of 134Cs and roots. Seedlings of maize (Zea mays L. cv Corso) were grown for 14days in solution culture and then transferred to a two-compartment pot system, where a single root was grown in a 134Cs contaminated compartment while the rest of the root system was grown in an uncontaminated compartment. Plants with the whole root system growing in a solution contaminated with 134Cs were used as control. We tested the effect of the competition between Cs and K on the uptake and translocation of 134Cs by using two K concentrations, 0.2 and 1.05mM. At the K concentration of the nutrient solution of 0.2mM the single root representing 21% of the total root weight was able to take up 47% of the 134Cs taken up by the entire root system, while at 1.05mM the single root, representing 15% of the total root weight, took up 15% of the 134Cs taken up by the entire root system. The translocation of 134Cs from the root to the shoots did not depend on the external K concentration in the nutrient solution, but it was lower in the split root treatment than in the control treatment at both K concentration

Stabilité d'une structure spatiale et compromis d'une analyse statistique multi-tableaux : application à la physico-chimie d'un lac réservoir

10 paramètres physico-chimiques sont mesurés en surface dans 10 stations à 12 dates sur le lac réservoir de la Sorme (Saône-et-Loire). L'article montre comment une analyse multitableaux peut caractériser la structure spatiale et préciser sa stabilité. Les notions d'interstructure et de compromis sont accessibles par une procédure simple et efficace.This paper is based on the observation that three-dimensional data matrices (sites x times x variables) often used in limnological investigations require statistical analyses fitted to experimental objectives. Many apparently different statistical tools (3-mode PCA of TUCKER, 1964; KROONENBERG, 1983; projection of variables WILLIAMS and STEPHENSON, 1973; DOLEDEC and CHESSEL, 1987) may be useful to clarify limnological problems such as : 1) the temporal variability of a pattern (elimination of spatial heterogenity) : 2) the spatial structure of a pattern (elimination of temporal effects, mapping of an average situation) : 3) the temporal variability of Lake stratification (stability, modification or inversion) : 4) the spatial structure of temporal variability, and 5) the between variables typology of a spatial and temporal structure. Our methodological approach allowed us to assess the temporal stability of the spatial structure of the Lake waters (question 3) using a multitable analysis known as triadic analysis (THIOULOUSE and CHESSEL, 1987).As part of the limnological study of a reservoir Lake (Sorme reservoir Lake, Saône-et-Loire, France) 10 commonly used physical and chemical variables were studied from July 1980 to October 1931. During this period, 12 water samples were taken near the surface at each of the 10 stations scattered along the Sorme Lake (see figure 1). Main morphometric features of the Sorme Lake are : 1) a surface area equal to 230 ha, 2) a 25 km long perimeter and 3) a volume of 9.5 106 m3 with a maximum depth of 13 meters upstream of the dam and an average depth of about 4 meters. Seasonal tidal range was only a few meters.Only 2 of the 3 concepts of triadic analysis stated by THIOULOUSE and CHESSEL, 1987 are developed here : 1) for each of the 12 tables (stations x variables) coming from the 12 sampling dates, data are first centered (elimination of mean) and standardized (division by standard deviation) (see figure 2). The resulting table Y called interstructure matrix, i.e. interstructure between each of the sampling dates matrix, is organized to have sampling dates as columns and the ten physical and chemical variables at each station successively as fines. Principal Component Analysis (PCA on the variance-covariance matrix) is then applied to the interstructure matrix. In our case it is a one-dimensional matrix, i.e. according to physical and chemical variables, there is only one spatial structure common to each sampling date (figure 3 and 2) compromise matrix are associated with the successive PCA factors of the interstructure (figure 4). According to the previous remark, only the first factor is considered. Data are reorganized to have physical and chemical variables as columns, and stations as fines. This last table defines a compromise matrix labelled Z. The mapping of the numerical values of matrix Z renders a ten-dimensional description of the permanent spatial structure (figure 5). To summarize the multivariate description, matrix Z is processed with a PCA on the variance-covariance matrix producing a three-dimensional compromise (figure 6).The interpretation of the compromise table by mapping the factorial scores of the PCA leads to a functional scheme of the reservoir Lake waters distinguishing five sectors (see figure 7) as a function of water depth, influence of tidal range, influence of tributaries and of the Sorme River. 3 stations are periodically isolated from the reservoir and produce 3 sectors with lower pH and temperature values and higher concentrations in ammonia and sulphate according to the influence of tributaries. The 4th sector is associated with the former submerged valley, i.e. main channel of the Sorme River prior to the dam closure, and demonstrated an ionic gradient concerning mainly nitrate and chloride-concentrations. The 5th sector, opposed to the latter, consists in the deeper area of the Sorme Lake which reveals rather homogeneous waters near the surface

A colossal atrial myxoma

Atrial myxomas are the most common benign primary tumor of the heart. These cardiac growths can masquerade as mitral stenosis and infective endocarditis. A 35-year-old man presented with complaints of nonspecific symptoms. Echocardiogram revealed a large atrial myxoma occupying the left atrium. Excision revealed a 14 × 8 × 6 cm3 tumor attached to a 4 × 3 × 2 cm3 stalk of septal tissue. We describe a giant left atrial myxoma. We were not able to find another myxoma as big as this one in the literature, so we are reporting it

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named as S-LASSO, is proposed for the coefficient function of a functional linear regression model where values of the response function, at a given domain point, depends on the full trajectory of the covariate function. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating regions where the coefficient function is zero, and to smoothly estimate non-zero values of the coefficient function. The sparsity of the estimator is ensured by a functional LASSO penalty whereas the smoothness is provided by two roughness penalties. The resulting estimator is proved to be estimation and pointwise sign consistent. Via an extensive Monte Carlo simulation study, the estimation and predictive performance of the S-LASSO estimator are shown to be better than (or at worst comparable with) competing estimators already presented in the literature before. Practical advantages of the S-LASSO estimator are illustrated through the analysis of the well known \textit{Canadian weather} and \textit{Swedish mortality dat

Functional clustering methods for resistance spot welding process data in the automotive industry

Quality assessment of resistance spot welding (RSW) joints of metal sheets in the automotive industry is typically based on costly and lengthy off-line tests that are unfeasible on the full production, especially on large scale. However, the massive industrial digitalization triggered by the industry 4.0 framework makes available, for every produced joint, on-line RSW process parameters, such as, in particular, the so-called dynamic resistance curve (DRC), which is recognized as the full technological signature of the spot welds. Motivated by this context, the present paper means to show the potentiality and the practical applicability to clustering methods of the functional data approach that avoids the need for arbitrary and often controversial feature extraction to find out homogeneous groups of DRCs, which likely pertain to spot welds sharing common mechanical and metallurgical properties. We intend is to provide an essential hands-on overview of the most promising functional clustering methods, and to apply the latter to the DRCs collected from the RSW process at hand, even if they could go far beyond the specific application hereby investigated. The methods analyzed are demonstrated to possibly support practitioners along the identification of the mapping relationship between process parameters and the final quality of RSW joints as well as, more specifically, along the priority assignment for off-line testing of welded spots and the welding tool wear analysis. The analysis code, that has been developed through the software environment R, and the DRC data set are made openly available online at https://github.com/unina-sfere/funclustRSW

Interleukin-1beta tear concentration in glaucomatous and ocular hypertensive patients treated with preservative-free nonselective beta-blockers

PURPOSE: To evaluate the ocular surface inflammatory response to the presence of preservatives in nonselective beta-blocker eyedrops. DESIGN: Prospective, crossover, single-masked, randomized clinical study. METHODS: STUDY POPULATION: Twenty primary open angle glaucoma or ocular hypertensive patients were divided in two groups, one treated with preservative-free timolol 0.5% (group 1) and the other with preserved timolol 0.5% (group 2) eyedrops. After 60 days of therapy and 3 more weeks of washout, the two groups switched to the other therapy. PROCEDURE: At each visit,basal tear samples were collected from the inferior conjunctival fornix for the determination of interleukin (IL)-1 tear concentrations by an enzyme-linked immunosorbent assay. Intraocular pressure measurement, conjunctival hyperemia, superficial punctate keratitis, and tear film breakup time were evaluated. MAIN OUTCOME MEASURE: IL-1 concentration in tears following the use of preserved eyedrops. RESULTS: IL-1 tear concentrations increased significantly in both groups, compared with baseline values,during preserved timolol therapy. There were no statistically significant changes in hyperemia and superficial punctate keratitis throughout the study in either group.A statistically significant breakup time reduction was observed in both groups after 30 days and after 60 days of preserved therapy. CONCLUSION: The use of preservatives in timolol 0.5% eyedrops leads to tear film instability and ocular surface inflammatory changes documented by a reduction of breakup time and an increase of IL-1 tear concentrations.Preservative-free beta-blockers are preferable for long-term hypotensive therapy to prevent ocular surface inflammation

Interleukin-1beta tear concentration in glaucomatous and ocular hypertensive patients treated with preservative-free nonselective beta-blockers

PURPOSE: To evaluate the ocular surface inflammatory response to the presence of preservatives in nonselective beta-blocker eyedrops. DESIGN: Prospective, crossover, single-masked, randomized clinical study. METHODS: STUDY POPULATION: Twenty primary open angle glaucoma or ocular hypertensive patients were divided in two groups, one treated with preservative-free timolol 0.5% (group 1) and the other with preserved timolol 0.5% (group 2) eyedrops. After 60 days of therapy and 3 more weeks of washout, the two groups switched to the other therapy. PROCEDURE: At each visit,basal tear samples were collected from the inferior conjunctival fornix for the determination of interleukin (IL)-1 tear concentrations by an enzyme-linked immunosorbent assay. Intraocular pressure measurement, conjunctival hyperemia, superficial punctate keratitis, and tear film breakup time were evaluated. MAIN OUTCOME MEASURE: IL-1 concentration in tears following the use of preserved eyedrops. RESULTS: IL-1 tear concentrations increased significantly in both groups, compared with baseline values,during preserved timolol therapy. There were no statistically significant changes in hyperemia and superficial punctate keratitis throughout the study in either group.A statistically significant breakup time reduction was observed in both groups after 30 days and after 60 days of preserved therapy. CONCLUSION: The use of preservatives in timolol 0.5% eyedrops leads to tear film instability and ocular surface inflammatory changes documented by a reduction of breakup time and an increase of IL-1 tear concentrations.Preservative-free beta-blockers are preferable for long-term hypotensive therapy to prevent ocular surface inflammation