Computing a Link Diagram from Its Exterior

A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by planar diagrams, whereas their exteriors, which are compact 3-manifolds with torus boundary, are encoded by triangulations. Here, we give the first practical algorithm for finding a diagram of a knot given a triangulation of its exterior. Our method applies to links as well as knots, allows us to recover links with hundreds of crossings. We use it to find the first diagrams known for 23 principal congruence arithmetic link exteriors; the largest has over 2,500 crossings. Other applications include finding pairs of knots with the same 0-surgery, which relates to questions about slice knots and the smooth 4D Poincar\'e conjecture.Comment: 34 pages, 29 figures; V2 minor changes incorporating referees' comments; to appear in "Proceedings of the 38th International Symposium on Computational Geometry (SoCG 2022)

Durable disease regression with copanlisib treatment in PI3K-mutated metastasizing ameloblastoma: A case report

Ameloblastoma is a rare tumor arising from odontogenic cells that is benign, yet locally aggressive. Metastasizing ameloblastoma (METAM) is an ultra-rare ameloblastoma variant in which both primary and secondary tumors have histological features of benign ameloblastoma. This is a case report of a patient who presented with a jaw mass and subsequent lung metastases, later diagnosed as METAM. Initial treatments, including carboplatin, etoposide, and taxane-based chemotherapy, were ineffective. Molecular profiling revealed mutations including PIK3CA H1047R and BRAF V600E. The patient was enrolled in a tumor-agnostic trial and began treatment with copanlisib, a PI3K inhibitor, which resulted in a partial response and durable disease regression. After 76 cycles, she continues to tolerate therapy well with minimal adverse events. This case highlights the potential of targeted therapies such as copanlisib for treating METAM, providing a promising therapeutic option for patients with PIK3CA mutations

Immunologic Gene Signature Analysis Correlates Myeloid Cells and M2 Macrophages with Time to Trabectedin Failure in Sarcoma Patients

Patients with metastatic soft tissue sarcoma (STS) have a poor prognosis and few available systemic treatment options. Trabectedin is currently being investigated as a potential adjunct to immunotherapy as it has been previously shown to kill tumor-associated macrophages. In this retrospective study, we sought to identify biomarkers that would be relevant to trials combining trabectedin with immunotherapy. We performed a single-center retrospective study of sarcoma patients treated with trabectedin with long-term follow-up. Multiplex gene expression analysis using the NanoString platform was assessed, and an exploratory analysis using the lasso-penalized Cox regression and kernel association test for survival (MiRKAT-S) methods investigated tumor-associated immune cells and correlated their gene signatures to patient survival. In total, 147 sarcoma patients treated with trabectedin were analyzed, with a mean follow-up time of 5 years. Patients with fewer prior chemotherapy regimens were more likely to stay on trabectedin longer (pairwise correlation = −0.17, p = 0.04). At 5 years, increased PD-L1 expression corresponded to worse outcomes (HR = 1.87, p = 0.04, q = 0.199). Additionally, six immunologic gene signatures were associated with up to 7-year survival by MiRKAT-S, notably myeloid-derived suppressor cells (p = 0.023, q = 0.058) and M2 macrophages (p = 0.03, q = 0.058). We found that the number of chemotherapy regimens prior to trabectedin negatively correlated with the number of trabectedin cycles received, suggesting that patients may benefit from receiving trabectedin earlier in their therapy course. The correlation of trabectedin outcomes with immune cell infiltrates supports the hypothesis that trabectedin may function as an immune modulator and supports ongoing efforts to study trabectedin in combination with immunotherapy. Furthermore, tumors with an immunosuppressive microenvironment characterized by macrophage infiltration and high PD-L1 expression were less likely to benefit from trabectedin, which could guide clinicians in future treatment decisions.</jats:p