A data driven equivariant approach to constrained Gaussian mixture modeling

Maximum likelihood estimation of Gaussian mixture models with different class-specific covariance matrices is known to be problematic. This is due to the unboundedness of the likelihood, together with the presence of spurious maximizers. Existing methods to bypass this obstacle are based on the fact that unboundedness is avoided if the eigenvalues of the covariance matrices are bounded away from zero. This can be done imposing some constraints on the covariance matrices, i.e. by incorporating a priori information on the covariance structure of the mixture components. The present work introduces a constrained equivariant approach, where the class conditional covariance matrices are shrunk towards a pre-specified matrix Psi. Data-driven choices of the matrix Psi, when a priori information is not available, and the optimal amount of shrinkage are investigated. The effectiveness of the proposal is evaluated on the basis of a simulation study and an empirical example

Density modelling with functional data analysis

[EN] Recent technological advances have eased the collection of big amounts of data in many research fields. In this scenario density estimation may represent an important source of information. One dimensional density functions represent a special case of functional data subject to the constraints to be non-negative and with a constant integral equal to one. Because of these constraints, a naive application of functional data analysis (FDA) methods may lead to non-valid results. To solve this problem, by means of an appropriate transformation, densities are embedded in the Hilbert space of square integrable functions where standard FDA methodologies can be applied.Gattone, SA.; Di Battista, T. (2023). Density modelling with functional data analysis. Editorial Universitat Politècnica de València. 87-91. https://doi.org/10.4995/CARMA2023.2023.16467879

Quantitative Renal Vascular Casting in Nephrology Research

The present paper describes the use of a quantitative renal vascular casting method to study the changes associated with kidney disease. Several animal models of hypertension (spontaneously hypertensive rat, SHR, with its normotensive rat the Wistar Kyoto, WKY; Dahl salt sensitive DS - hypertensive, and salt resistant DR -normotensive) were examined at time points when the systemic blood pressure was rising (6 and 12 weeks of age) and following renal denervation (in SHR-WKY rats). The SHR appears to have a smaller caliber afferent arteriole at both 6 and 12 weeks of age. This difference is probably not entirely due to sympathetic vasoconstriction since the strain related afferent arteriolar diameter difference was still present after renal denervation. In the Dahl rats, there is not much of an intrarenal vascular difference between the DS and DR rats with the only real finding of a smaller distal afferent arteriolar diameter found in outer cortical nephrons of the DR. The two models of acute renal failure (ARF) that were studied include, a) the glycerol model (known to initially cause an intense vasoconstriction) and b) gentamicin, a nephrotoxic antibiotic. Two time points were examined for each of these models. As expected in the glycerol model there was an intense vasoconstriction at three hours which essentially was gone at 3 days-a time when the renal failure was fulminant. The glomerulus appeared to be contracted at three hours as well. In the gentamicin model no renal vascular alteration was seen at 6 days, when renal failure was mild while at 10 days, when renal failure was pronounced, outer cortical afferent arterioles appeared to be moderately constricted. In the 5/6 nephrectomy model of chronic renal failure, the glomeruli were smaller in rats in renal failure than in the controls

Chapter Profiling visitors of a national park in Italy through unsupervised classification of mixed data

Cluster analysis has for long been an effective tool for analysing data. Thus, several disciplines, such as marketing, psychology and computer sciences, just to mention a few, did take advantage from its contribution over time. Traditionally, this kind of algorithm concentrates only on numerical or categorical data at a time. In this work, instead, we analyse a dataset composed of mixed data, namely both numerical than categorical ones. More precisely, we focus on profiling visitors of the National Park of Majella in the Abruzzo region of Italy, which observations are characterized by variables such as gender, age, profession, expectations and satisfaction rate on park services. Applying a standard clustering procedure would be wholly inappropriate in this case. Therefore, we hereby propose an unsupervised classification of mixed data, a specific procedure capable of processing both numerical than categorical variables simultaneously, releasing truly precious information. In conclusion, our application therefore emphasizes how cluster analysis for mixed data can lead to discover particularly informative patterns, allowing to lay the groundwork for an accurate customers profiling, starting point for a detailed marketing analysis

Quantitative Vascular Casting of the Post-Ischemic Hydronephrotic Kidney

The renal microvasculature (afferent arteriole) and glomeruli were examined and quantitated by two methods in the post-ischemic hydronephrotic (PIH) kidney. The methods used were: 1) an in vivo examination and 2) controlled perfusion-fixation, quantitative vascular casting examined by scanning electron microscopy. The second method was also applied to the vasculature of the contralateral, functional kidney. The goals of the study were to: 1) validate the quantitative vascular casting method by comparing PIH renal microvascular data from the casting method with in vivo values and 2) determine the extent of microvascular dimensional difference of the PIH kidney from its contralateral functional counterpart. It was determined that the casting values were consistent with the data obtained from the in vivo examination of the afferent arteriole and glomeruli. This finding provides further support for the quantitative renal microvascular casting technique. Using that technique it was determined that the dimensions of the microvasculature and glomeruli of the PIH kidney were severely (and significantly, p\u3c0.05) reduced compared to its functional mate. Since these PIH vessels show a significant decrement in size, vascular reactivity and functional data based on the PIH vessels should be looked at cautiously. The vasculature and glomeruli of the PIH kidney might not be totally normal, however structurally, the glomeruli do not appear to be dramatically altered

A Measure of Variability for the Customer Satisfaction Index

EnIn this paper we deal with the problem of identifying heterogeneity indices for the purpose of improving the analysis of customer satisfaction observing the phenomenon through a new perspective. Our work introduces some indices that may be used for measuring heterogeneity in Customer Satisfaction framework and an application on real data is illustrated

Relativistic Two-Body Processes in Axial-Charge Transitions

We study the contribution of two-body meson-exchange processes to axial charge transitions for nuclei in the lead, tin and oxygen regions. We conduct calculations in the Dirac-Hartree (the Walecka model) and the relativistic Hartree (where the full one-nucleon-loop effects are included) approximations. We present results indicating that one- and two-body processes enhance the matrix elements of the axial-charge operator by some (100+-20)% in all three regions studied. This agrees well with the fit of eighteen first-forbidden beta-decay transitions conducted by Warburton in the lead region. We also discuss some sensitivities present in the calculation.Comment: 23 pages, RevTeX format, 5 PostScript figures available on reques