Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Real-world data on incidence, clinical characteristics and outcome of patients with macrofocal multiple myeloma (MFMM) in the era of novel therapies: A study of the Greco-Israeli collaborative myeloma working group

We investigated incidence, characteristics and outcome of patients with macrofocal multiple myeloma (MFMM) treated mainly with novel therapies. Based on definition (BMPCs <20% and lytic lesions/plasmacytomas, without anemia, renal insufficiency or hypercalcemia) we identified 140 patients with MFMM, among 4650 myeloma patients (3%). Twice the number of patients with typical myeloma were used as controls; 60% were <65 years and 70% had advanced bone disease. Plasmacytomas were more frequent in MFMM compared with standard myeloma (68% vs 15%, P <.05). Adverse prognostic parameters (high lactate dehydrogenase, advanced stage, high risk cytogenetics, immunoparesis) were less common in patients with MFMM compared with controls (P <.05); 90% received novel agents and 47% underwent autologous transplantation upfront; 90% achieved an objective response; 70% had at least very good partial response which was significantly higher compared with controls (P <.05). After a median follow-up of 52 months, 33 patients have died. Early death (<12 months) was infrequent in MFMM. Median progression-free survival and overall survival (OS) were 46 and 129 months respectively, both significantly longer compared with controls (P <.001). Proteasome inhibitor (PI)-based therapy was the only independent predictor for OS in the multivariate analysis (HR: 3.9; P <.001). In conclusion, MFMM is a distinct entity presented in young and elderly subjects, characterized by limited bone marrow infiltration, advanced bone disease and frequent presence of plasmacytomas; MFMM patients have less often adverse prognostic features and achieve excellent responses and prolonged OS especially when treated with PI-based therapies. Novel imaging will help in a more accurate classification of this entity. © 2020 Wiley Periodicals, Inc