On the symbolic powers of binomial edge ideals

We show that under some conditions, if the initial ideal in$_<(I)$ of an ideal $I$ in a polynomial ring has the property that its symbolic and ordinary powers coincide, then the ideal $I$ shares the same property. We apply this result to prove the equality between symbolic and ordinary powers for binomial edge ideals with quadratic Gr\"obner basis

International Prognostic Score for Nodular Lymphocyte-Predominant Hodgkin Lymphoma

\ua9 American Society of Clinical Oncology.PURPOSENodular lymphocyte-predominant Hodgkin lymphoma (NLPHL) is a rare cancer, and large international cooperative efforts are needed to evaluate the significance of clinical risk factors and immunoarchitectural patterns (IAPs) for all stages of pediatric and adult patients with NLPHL.METHODSThirty-eight institutions participated in the Global nLPHL One Working Group retrospective study of NLPHL cases from 1992 to 2021. We measured progression-free survival (PFS), overall survival (OS), transformation rate, and lymphoma-specific death rate. We performed uni- and multivariable (MVA) Cox regression stratified by management to select factors for the lymphocyte-predominant international prognostic score (LP-IPS) validated by five-fold cross-validation.RESULTSWe identified 2,243 patients with a median age of 37 years (IQR, 23-51). The median follow-up was 6.3 years (IQR, 3.4-10.8). Most had stage I to II (72.9%) and few B symptoms (9.9%) or splenic involvement (5.4%). IAP was scored for 916 (40.8%). Frontline management included chemotherapy alone (32.4%), combined modality therapy (30.5%), radiotherapy alone (24.0%), observation after excision (4.6%), rituximab alone (4.0%), active surveillance (3.4%), and rituximab and radiotherapy (1.1%). The PFS, OS, transformation, and lymphoma-specific death rates at 10 years were 70.8%, 91.6%, 4.8%, and 3.3%, respectively. On MVA, IAPs were not associated with PFS or OS, but IAP E had higher risk of transformation (hazard ratio [HR], 1.81; P &lt;.05). We developed the LP-IPS with 1 point each for age ≥45 years, stage III-IV, hemoglobin &lt;10.5 g/dL, and splenic involvement. Increasing LP-IPS was significantly associated with worse PFS (HR, 1.52) and OS (HR, 2.31) and increased risk of lymphoma-specific death (HR, 2.63) and transformation (HR, 1.41).CONCLUSIONIn this comprehensive study of all ages of patients with NLPHL, we develop the LP-IPS to identify high-risk patients and inform upcoming prospective clinical trials evaluating de-escalation of therapy for patients with low LP-IPS scores (&lt;2)