New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the truncation error on the boundary points, the spectral radius, or a combination of these. We examine in detail a set of operators that are up to tenth order accurate in the interior, and we surprisingly find that a combination of these optimizations can improve the operators' spectral radius and accuracy by orders of magnitude in certain cases. We also construct high-order dissipation operators that are compatible with these new finite difference operators and which are semi-definite with respect to the appropriate summation by parts scalar product. We test the stability and accuracy of these new difference and dissipation operators by evolving a three-dimensional scalar wave equation on a spherical domain consisting of seven blocks, each discretized with a structured grid, and connected through penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the derivative and dissipation operators can be accessed by downloading the source code for the document. The files are located in the "coeffs" subdirector

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

Generation of donor-specific Tr1 cells to be used after kidney transplantation and definition of the timing of their in vivo infusion in the presence of immunosuppression

Background: Operational tolerance is an alternative to lifelong immunosuppression after transplantation. One strategy to achieve tolerance is by T regulatory cells. Safety and feasibility of a T regulatory type 1 (Tr1)-cell-based therapy to prevent graft versus host disease in patients with hematological malignancies has been already proven. We are now planning to perform a Tr1-cell-based therapy after kidney transplantation. Methods: Upon tailoring the lab-grade protocol to patients on dialysis, aims of the current work were to develop a clinical-grade compatible protocol to generate a donor-specific Tr1-cell-enriched medicinal product (named T10 cells) and to test the Tr1-cell sensitivity to standard immunosuppression in vivo to define the best timing of cell infusion. Results: We developed a medicinal product that was enriched in Tr1 cells, anergic to donor-cell stimulation, able to suppress proliferation upon donor- but not third-party stimulation in vitro, and stable upon cryopreservation. The protocol was reproducible upon up scaling to leukapheresis from patients on dialysis and was effective in yielding the expected number of T10 cells necessary for the planned infusions. The tolerogenic gene signature of circulating Tr1 cells was minimally compromised in kidney transplant recipients under standard immunosuppression and it eventually started to recover 36weeks post-transplantation, providing rationale for selecting the timings of the cell infusions. Conclusions: These data provide solid ground for proceeding with the trial and establish robust rationale for defining the correct timing of cell infusion during concomitant immunosuppressive treatment

On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations

We give a well posed initial value formulation of the Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge conditions given by a Bona-Masso like slicing condition for the lapse and a frozen shift. This is achieved by introducing extra variables and recasting the evolution equations into a first order symmetric hyperbolic system. We also consider the presence of artificial boundaries and derive a set of boundary conditions that guarantee that the resulting initial-boundary value problem is well posed, though not necessarily compatible with the constraints. In the case of dynamical gauge conditions for the lapse and shift we obtain a class of evolution equations which are strongly hyperbolic and so yield well posed initial value formulations

Assessment of myocardial extracellular volume on body computed tomography in breast cancer patients treated with anthracyclines

Background: Cancer treatment with anthracyclines may lead to an increased incidence of cardiac disease due to cardiotoxicity, as they may cause irreversible myocardial fibrosis. So far, the proposed methods for screening patients for cardiotoxicity have led to only limited success, while the analysis of myocardial extracellular volume (mECV) at cardiac magnetic resonance (CMR) has shown promising results, albeit requiring a dedicated exam. Recent studies have found strong correlations between mECV values obtained through computed tomography (CT), and those derived from CMR. Thus, our purpose was to evaluate the feasibility of estimating mECV on thoracic contrast-enhanced CT performed for staging or follow-up in breast cancer patients treated with anthracyclines, and, if feasible, to assess if a rise in mECV is associated with chemotherapy, and persistent over time. Methods: After ethics committee approval, female patients with breast cancer who had undergone at least 2 staging or follow-up CT examinations at our institution, one before and one shortly after the end of chemotherapy including anthracyclines were retrospectively evaluated. Patients without available haematocrit, with artefacts in CT images, or who had undergone radiation therapy of the left breast were excluded. Follow-up CT examinations at longer time intervals were also analysed, when available. mECV was calculated on scans obtained at 1, and 7 min after contrast injection. Results: Thirty-two female patients (aged 57\ub113 years) with pre-treatment haematocrit 38%\ub14%, and ejection fraction 64%\ub16% were analysed. Pre-treatment mECV was 27.0%\ub12.9% at 1 min, and 26.4%\ub13.8% at 7 min, similar to values reported for normal subjects in the literature. Post-treatment mECV (median interval: 89 days after treatment) was 31.1%\ub14.9%, and 30.0%\ub15.1%, respectively, values significantly higher than pre-treatment values at all times (P&lt;0.005). mECV at follow-up (median interval: 135 days after post-treatment CT) was 31.0%\ub14.5%, and 27.7%\ub13.7%, respectively, without significant differences (P&gt;0.548) when compared to post-treatment values. Conclusions: mECV values from contrast-enhanced CT scans could play a role in the assessment of myocardial condition in breast cancer patients undergoing anthracycline-based chemotherapy. CT-derived ECV could be an imaging biomarker for the monitoring of therapy-related cardiotoxicity, allowing for potential secondary prevention of cardiac damage, using data derived from an examination that could be already part of patients\u2019 clinical workflow

Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids

We consider the flow of an upper convected Maxwell fluid in the limit of high Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be imposed on the solutions. We derive equations for the resulting boundary layer and prove the well-posedness of these equations. A transformation to Lagrangian coordinates is crucial in the argument