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Epithelioid sarcoma is a rare and aggressive mesenchymal tumour, the genetic hallmark of which is the loss of expression of SMARCB1, a key member of the SWItch/Sucrose Non‐Fermentable (SWI/SNF) chromatin remodelling complex. Hampered by its rarity, epithelioid sarcoma has received little research attention and therapeutic options for this disease remain limited. SMARCB1‐deficient tumours also include malignant rhabdoid tumour, atypical teratoid and rhabdoid tumour, epithelioid malignant peripheral nerve sheath tumour, and poorly differentiated chordoma. Histologically, it can be challenging to distinguish epithelioid sarcoma from malignant rhabdoid tumour and other SMARCB1‐deficient tumours, whereas methylation profiling shows that they represent distinct entities and facilitates their classification. Methylation studies on SMARCB1‐deficient tumours, although not including epithelioid sarcomas, reported methylation subgroups which resulted in new clinical stratification and therapeutic approaches. In addition, emerging evidence indicates that immunotherapy, including immune checkpoint inhibitors, represents a promising therapeutic strategy for SMARCB1‐deficient tumours. Here, we show that some epithelioid sarcomas share methylation patterns of malignant rhabdoid tumours indicating that this could help to distinguish these entities and guide treatment. Using gene expression data, we also showed that the immune environment of epithelioid sarcoma is characterised by a predominance of CD8+ lymphocytes and M2 macrophages. These findings have potential implications for the management of patients with epithelioid sarcoma. © 2023 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of The Pathological Society of Great Britain and Ireland. [ABSTRACT FROM AUTHOR]

We consider an elliptic self-adjoint first-order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact three-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the manifold, with summation carried out over all eigenvalues between zero and a positive $\lambda$. We derive an explicit two-term asymptotic formula for the spectral function as $\lambda \to + \infty$, expressing the second asymptotic coefficient via the trace of the subprincipal symbol and the geometric objects encoded within the principal symbol-metric, torsion of the teleparallel connection and topological charge. We then address the question: is our operator a massless Dirac operator on half-densities? We prove that it is a massless Dirac operator on half-densities if and only if the following two conditions are satisfied at every point of the manifold: (a) the subprincipal symbol is proportional to the identity matrix; and (b) the second asymptotic coefficient of the spectral function is zero. [ABSTRACT FROM AUTHOR]