A space–time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation

We introduce a space–time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one-dimensional scheme of Kretzschmar et al. (IMA J Numer Anal 36:1599–1635, 2016). Test and trial discrete functions are space–time piecewise polynomial solutions of the wave equations. We prove well-posedness and a priori error bounds in both skeleton-based and mesh-independent norms. The space–time formulation corresponds to an implicit time-stepping scheme, if posed on meshes partitioned in time slabs, or to an explicit scheme, if posed on “tent-pitched” meshes. We describe two Trefftz polynomial discrete spaces, introduce bases for them and prove optimal, high-order h-convergence bounds

Minimal residual disease evaluation by flow cytometry is a complementary tool to cytogenetics for treatment decisions in acute myeloid leukaemia

For PETHEMA Programa para el Estudio de la Terapéutica en Hemopatías Malignas Cooperative Study Group.The clinical utility of minimal residual disease (MRD) analysis in acute myeloid leukaemia (AML) is not yet defined. We analysed the prognostic impact of MRD level at complete remision after induction therapy using multiparameter flow cytometry in 306 non-APL AML patients. First, we validated the prognostic value of MRD-thresholds we have previously proposed (≥0.1%; ≥0.01-0.1%; and <0.01), with a 5-year RFS of 38%, 50% and 71%, respectively (p = 0.002). Cytogenetics is the most relevant prognosis factor in AML, however intermediate risk cytogenetics represent a grey zone that require other biomarkers for risk stratification, and we show that MRD evaluation discriminate three prognostic subgroups (p = 0.03). Also, MRD assessments yielded relevant information on favourable and adverse cytogenetics, since patients with favourable cytogenetics and high MRD levels have poor prognosis and patients with adverse cytogenetics but undetectable MRD overcomes the adverse prognosis. Interestingly, in patients with intermediate or high MRD levels, intensification with transplant improved the outcome as compared with chemotherapy, while the type of intensification therapy did not influenced the outcome of patients with low MRD levels. Multivariate analysis revealed age, MRD and cytogenetics as independent variables. Moreover, a scoring system, easy in clinical practice, was generated based on MRD level and cytogenetics.This work was supported in part by Spanish grants from Fondo de Investigación Sanitaria-ISCIII (FIS 00/0023-03, PI12/02321), DGCYT (SAF 94- 0308, SAF2001-1687), Conserjería de Educación de Castilla y León (HUS416A12), and Red Temática de Investigación Cooperativa en Cáncer (RTICC-ISCIII) (RD12/0036/0069).Peer Reviewe

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces