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We show that the eigenschemes of 4 x 4 x 4 symmetric tensors are parameterized by a linear subvariety of the Grassmannian Gr(3;ℙ14). We also study the decomposition of the eigenscheme into the subscheme associated to the zero eigenvalue and its residue. In particular, we describe the possible degrees and dimensions. [ABSTRACT FROM AUTHOR]

Prostate cancer ranks among the most prevalent tumours globally. While early detection reduces the likelihood of metastasis, managing advanced cases poses challenges in diagnosis and treatment. Current international guidelines support the concurrent use of 99 Tc-Bone Scintigraphy and Contrast-Enhanced Chest and Abdomen CT for the staging of metastatic disease and response assessment. However, emerging evidence underscores the superiority of next-generation imaging techniques including PSMA-PET/CT and whole-body MRI (WB-MRI). This review explores the relevant scientific literature on the role of WB-MRI in metastatic prostate cancer. This multiparametric imaging technique, combining the high anatomical resolution of standard MRI sequences with functional sequences such as diffusion-weighted imaging (DWI) and bone marrow relative fat fraction (rFF%) has proved effective in comprehensive patient assessment, evaluating local disease, most of the nodal involvement, bone metastases and their complications, and detecting the increasing visceral metastases in prostate cancer. It does have the advantage of avoiding the injection of contrast medium/radionuclide administration, spares the patient the exposure to ionizing radiation, and lacks the confounder of FLARE described with nuclear medicine techniques. Up-to-date literature regarding the diagnostic capabilities of WB-MRI, though still limited compared to PSMA-PET/CT, strongly supports its widespread incorporation into standard clinical practice, alongside the latest nuclear medicine techniques.

The Testicular Juvenile Granulosa Cell Tumor (JGCT) is a rare testicular neoplasm that appears in the first months of life as a painless testicular mass. Following an accurate radiological ultrasound diagnosis, through which the cystic appearance of the lesion is observed, and histological confirmation, showing follicular growth pattern and an immunoreactivity for inhibin, the treatment process involves, when feasible, conservative surgery. We present the case of a 2-months old infant with a bilateral JGCT of the testis and we review the classical findings of the patology., (© 2024. Società Italiana di Ultrasonologia in Medicina e Biologia (SIUMB).)