Bures volume of the set of mixed quantum states

We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte

Diagnostic Value of 18F-fluorodeoxyglucose Positron Emission Tomography with Computed Tomography for Lymph Node Staging in Patients with Upper Tract Urothelial Carcinoma

BACKGROUND: Presence of lymph node metastases (LNM) is an important prognostic factor for cancer-specific survival (CSS) in patients with upper tract urothelial carcinoma (UTUC). In various neoplasms, 18F-fluorodeoxyglucose positron emission tomography with computed tomography (FDG-PET/CT) is an established modality for preoperative lymph node (LN) staging. In UTUC, the diagnostic value of FDG-PET/CT for LN staging is unknown. OBJECTIVE: To determine the diagnostic value of FDG-PET/CT for LN staging in patients with UTUC. DESIGN, SETTING, AND PARTICIPANTS: Data of 152 patients with UTUC who underwent FDG-PET/CT followed by surgical treatment in eight centers between 2007 and 2017 were retrospectively collected. Patients receiving neoadjuvant chemotherapy were excluded. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: FDG-PET/CT results were compared with histopathology after lymph node dissection (LND). Recurrence-free survival (RFS), CSS, and overall survival (OS) were analyzed using Kaplan-Meier estimates, and compared for patients with and without suspicious LNs on FDG-PET/CT. RESULTS AND LIMITATIONS: We included 117 patients, of whom 62 underwent LND. Seventeen patients had LNM at histopathological evaluation. Sensitivity and specificity of FDG-PET/CT for diagnosis of LNM were 82% (95% confidence interval [CI]: 57-96) and 84% (95% CI: 71-94), respectively. RFS was significantly worse in patients with LN-positive FDG-PET/CT than in those with LN-negative FDG-PET/CT (p=0.03). CSS (p=0.11) and OS (p=0.5) were similar between groups. This study is limited by its retrospective design and by its sample size. Our results warrant further validation. CONCLUSIONS: FDG-PET/CT has 82% sensitivity and 84% specificity for the detection of LNM in patients with UTUC. Presence of suspicious LNs on FDG-PET/CT is associated with worse RFS. PATIENT SUMMARY: In patients with upper tract urothelial cancer, positron emission tomography with computed tomography (PET/CT) scans can detect lymph node metastases with noteworthy accuracy. Presence of suspicious lymph nodes on 18F-fluorodeoxyglucose PET/CT is associated with worse recurrence-free survival

Genome-wide cell-free DNA fragmentation in patients with cancer

Cell-free DNA in the blood provides a non-invasive diagnostic avenue for patients with cancer1. However, characteristics of the origins and molecular features of cell-free DNA are poorly understood. Here we developed an approach to evaluate fragmentation patterns of cell-free DNA across the genome, and found that profiles of healthy individuals reflected nucleosomal patterns of white blood cells, whereas patients with cancer had altered fragmentation profiles. We used this method to analyse the fragmentation profiles of 236 patients with breast, colorectal, lung, ovarian, pancreatic, gastric or bile duct cancer and 245 healthy individuals. A machine learning model that incorporated genome-wide fragmentation features had sensitivities of detection ranging from 57% to more than 99% among the seven cancer types at 98% specificity, with an overall area under the curve value of 0.94. Fragmentation profiles could be used to identify the tissue of origin of the cancers to a limited number of sites in 75% of cases. Combining our approach with mutation-based cell-free DNA analyses detected 91% of patients with cancer. The results of these analyses highlight important properties of cell-free DNA and provide a proof-of-principle approach for the screening, early detection and monitoring of human cancer