Interpolation with the polynomial kernels

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness. In particular they do not enjoy the usual property of unisolvency for arbitrary point sets, which is one of the key properties used to build kernel-based interpolation methods. This paper is devoted to establish some initial results for the study of these kernels, and their related interpolation algorithms, in the context of approximation theory. We will first prove necessary and sufficient conditions on point sets which guarantee the existence and uniqueness of an interpolant. We will then study the Reproducing Kernel Hilbert Spaces (or native spaces) of these kernels and their norms, and provide inclusion relations between spaces corresponding to different kernel parameters. With these spaces at hand, it will be further possible to derive generic error estimates which apply to sufficiently smooth functions, thus escaping the native space. Finally, we will show how to employ an efficient stable algorithm to these kernels to obtain accurate interpolants, and we will test them in some numerical experiment. After this analysis several computational and theoretical aspects remain open, and we will outline possible further research directions in a concluding section. This work builds some bridges between kernel and polynomial interpolation, two topics to which the authors, to different extents, have been introduced under the supervision or through the work of Stefano De Marchi. For this reason, they wish to dedicate this work to him in the occasion of his 60th birthday

Epiphyseal Cleft: A Misleading Radiologic Finding

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A Real-time Cerebral Bleeding in an Extremely Preterm Newborn

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The first Italian COVID-19 lockdown reduced births and voluntary terminations by just under a fifth

No abstract available

Special Issue dedicated to Stefano De Marchi on the occasion of his 60th birthday

As colleagues and friends we dedicate this issue to Stefano De Marchi on the occasion of his 60th birthday, publishing works of some of his collaborators. Stefano has made many important contributions to approximation theory and beyond and is one of the “founding fathers” of this journal. Here we briefly reminisce and recount some of our experiences with Stefano in the spirit of the occasion

Cholesteatoma vs granulation tissue: a differential diagnosis by DWI-MRI apparent diffusion coefficient

To diagnose cholesteatoma when it is not visible through tympanic perforation, imaging techniques are necessary. Recently, the combination of computed tomography and magnetic resonance imaging has proven effective to diagnose middle ear cholesteatoma. In particular, diffusion weighted images have integrated the conventional imaging for the qualitative assessment of cholesteatoma. Accordingly, the aim of this study was to obtain a quantitative analysis of cholesteatoma calculating the apparent diffusion coefficient value. So, we investigated whether it could differentiate cholesteatoma from other inflammatory tissues both in a preoperative and in a postoperative study

Brain Plasticity in Charcot-Marie-Tooth Type 1A Patients? A Combined Structural and Diffusion MRI Study

Central nervous system involvement has been described in peripheral neuropathies, including different forms of Charcot-Marie-Tooth (CMT) disease. The aim of our study was to systematically investigate possible brain structural modifications in CMT1A patients, using volumetric MRI, and diffusion tensor imaging (DTI). In this prospective cross-sectional study, from May 2017 to May 2019, we acquired 3T MRI brain scans of genetically confirmed CMT1A patients and age- and sex-comparable healthy controls. Patients also underwent clinical and electrophysiological examinations assessing motor and sensory domains. Voxel-based morphometry (VBM) and tract-based spatial statistics (TBSS) analyses were performed using a non-parametric approach based on permutations, including age and sex (and total intracranial volume for VBM) as nuisance covariates. When between-group differences emerged at VBM or TBSS analyses, the first eigenvariate was extracted from the cluster and its age- and sex-adjusted standardized residuals tested for correlation with clinical and electrophysiological variables. Twenty CMT1A patients (34.5 ± 11.1 years; M/F:11/9) were enrolled, along with 20 healthy controls (30.1 ± 10.2 years; M/F:11/9). The VBM analysis revealed clusters of significantly increased GM volume in CMT1A patients compared to healthy controls, encompassing the bilateral cerebellar lobules III-VI and the left hippocampus (all ps = 0.04), with no differences in terms of DTI metrics at the TBSS analysis. A negative correlation (r = −0.502, p = 0.03) emerged between ulnar compound motor action potential and the z-scores corresponding to the right cerebellar cluster of augmented GM volume. Our data show evidence of structural reorganization in the brain of CMT1A patients, possibly reflecting neural plasticity mechanisms in response to peripheral nerve pathology and modulating the effect of axonal degeneration on functional impairment

Frameless stereotactic biopsy for precision neurosurgery : diagnostic value, safety, and accuracy

BACKGROUND: Stereotactic biopsy is consistently employed to characterize cerebral lesions in patients who are not suitable for microsurgical resection. In the past years, technical improvement and neuroimaging advancements contributed to increase the diagnostic yield, the safety, and the application of this procedure. Currently, in addition to histological diagnosis, the molecular analysis is considered essential in the diagnostic process to properly select therapeutic and prognostic algorithms in a personalized approach. The present study reports our experience with frameless stereotactic brain biopsy in this molecular era. METHODS: One hundred forty consecutive patients treated from January 2013 to September 2018 were analyzed. Biopsies were performed using the Brainlab Varioguide\uae frameless stereotactic system. Patients' clinical and demographic data, the time of occupation of the operating room, the surgical time, the morbidity, and the diagnostic yield in providing a histological and molecular diagnosis were recorded and evaluated. RESULTS: The overall diagnostic yield was 93.6% with nine procedures resulting non-diagnostic. Among 110 patients with glioma, the IDH-1 mutational status was characterized in 108 cases (98.2%), resulting wild-type in all subjects but 3; MGMT methylation was characterized in 96 cases (87.3%), resulting present in 60 patients, and 1p/19q codeletion was founded in 6 of the 20 cases of grade II-III gliomas analyzed. All the specimens were apt for molecular analysis when performed. Bleeding requiring surgical drainage occurred in 2.1% of the cases; 8 (5.7%) asymptomatic hemorrhages requiring no treatment were observed. No biopsy-related mortality was recorded. Median length of hospital stay was 5 days (IQR 4-8) with mean surgical time of 60.77 min (\ub1\u200923.12) and 137.44\u2009\ub1\u200924.1 min of total occupation time of the operative room. CONCLUSIONS: Stereotactic frameless biopsy is a safe, feasible, and fast procedure to obtain a histological and molecular diagnosis

Skull Base Fungal Osteomyelitis: A Case Report and Review of the Literature

Skull base osteomyelitis (SBO) is an invasive infection refractory to therapy, closely linked with malignant otitis externa (MOE). It is characterized by a mild clinical presentation that can delay cross-sectional imaging considered as the key to revealing it. Skull base osteomyelitis typically affects elderly diabetics and immunocompromised patients (>70 years). It most commonly has an otogenic origin due to an extension of MOE. The prognosis can be very poor without the administration of adequate and timely therapy at an early disease stage. Nowadays, Pseudomonas aeruginosa remains the most common pathogen associated with SBO. Fungi are a rare cause of MOE. This report documents a rare case of otogenic SBO caused by Candida parapsilosis in a diabetic patient, with persistent otologic symptoms as clinical onset and resistance to medical treatment. Fungal MOE has more subtle symptoms and is more aggressive than its bacterial counterpart. When MOE is resistant to antibacterial drugs, this should raise the suspicion of a fungal etiology of MOE. The current guidelines do not exhaustively describe the diagnosis, antifungal drugs of choice, and optimum duration of treatment. The description of these rare clinical cases should help with the multidisciplinary management of this disease in order to optimize the diagnosis and therapeutic protocol