Nonlinear approximation in bounded orthonormal product bases

We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the function, where the corresponding basis support is assumed to be unknown. Our method is based on point evaluations of the considered function and adaptively builds an index set of a suitable basis support such that the approximately largest basis coefficients are still included. For this purpose, the algorithm only needs a suitable search space that contains the desired index set. Throughout the work, there are various minor modifications of the algorithm discussed as well, which may yield additional benefits in several situations. For the first time, we provide a proof of a detection guarantee for such an index set in the function approximation case under certain assumptions on the sub-methods used within our algorithm, which can be used as a foundation for similar statements in various other situations as well. Some numerical examples in different settings underline the effectiveness and accuracy of our method

The uniform sparse FFT with application to PDEs with random coefficients

We develop the uniform sparse Fast Fourier Transform (usFFT), an efficient, non-intrusive, adaptive algorithm for the solution of elliptic partial differential equations with random coefficients. The algorithm is an adaption of the sparse Fast Fourier Transform (sFFT), a dimension-incremental algorithm, which tries to detect the most important frequencies in a given search domain and therefore adaptively generates a suitable Fourier basis corresponding to the approximately largest Fourier coefficients of the function. The usFFT does this w.r.t. the stochastic domain of the PDE simultaneously for multiple fixed spatial nodes, e.g., nodes of a finite element mesh. The key idea of joining the detected frequency sets in each dimension increment results in a Fourier approximation space, which fits uniformly for all these spatial nodes. This strategy allows for a faster and more efficient computation due to a significantly smaller amount of samples needed, than just using other algorithms, e.g., the sFFT for each spatial node separately. We test the usFFT for different examples using periodic, affine and lognormal random coefficients in the PDE problems

Targeting cardiomyocyte ADAM10 ectodomain shedding promotes survival early after myocardial infarction

After myocardial infarction the innate immune response is pivotal in clearing of tissue debris as well as scar formation, but exaggerated cytokine and chemokine secretion with subsequent leukocyte infiltration also leads to further tissue damage. Here, we address the value of targeting a previously unknown a disintegrin and metalloprotease 10 (ADAM10)/CX3CL1 axis in the regulation of neutrophil recruitment early after MI. We show that myocardial ADAM10 is distinctly upregulated in myocardial biopsies from patients with ischemia-driven cardiomyopathy. Intriguingly, upon MI in mice, pharmacological ADAM10 inhibition as well as genetic cardiomycyte-specific ADAM10 deletion improves survival with markedly enhanced heart function and reduced scar size. Mechanistically, abolished ADAM10-mediated CX3CL1 ectodomain shedding leads to diminished IL-1β-dependent inflammation, reduced neutrophil bone marrow egress as well as myocardial tissue infiltration. Thus, our data shows a conceptual insight into how acute MI induces chemotactic signaling via ectodomain shedding in cardiomyocytes

CNP Promotes Antiarrhythmic Effects via Phosphodiesterase 2

Background: Ventricular arrhythmia and sudden cardiac death are the most common lethal complications after myocardial infarction. Antiarrhythmic pharmacotherapy remains a clinical challenge and novel concepts are highly desired. Here, we focus on the cardioprotective CNP (C-type natriuretic peptide) as a novel antiarrhythmic principle. We hypothesize that antiarrhythmic effects of CNP are mediated by PDE2 (phosphodiesterase 2), which has the unique property to be stimulated by cGMP to primarily hydrolyze cAMP. Thus, CNP might promote beneficial effects of PDE2-mediated negative crosstalk between cAMP and cGMP signaling pathways. Methods: To determine antiarrhythmic effects of cGMP-mediated PDE2 stimulation by CNP, we analyzed arrhythmic events and intracellular trigger mechanisms in mice in vivo, at organ level and in isolated cardiomyocytes as well as in human-induced pluripotent stem cell-derived cardiomyocytes. Results: In ex vivo perfused mouse hearts, CNP abrogated arrhythmia after ischemia/reperfusion injury. Upon high-dose catecholamine injections in mice, PDE2 inhibition prevented the antiarrhythmic effect of CNP. In mouse ventricular cardiomyocytes, CNP blunted the catecholamine-mediated increase in arrhythmogenic events as well as in ICaL, INaL, and Ca2+spark frequency. Mechanistically, this was driven by reduced cellular cAMP levels and decreased phosphorylation of Ca2+handling proteins. Key experiments were confirmed in human iPSC-derived cardiomyocytes. Accordingly, the protective CNP effects were reversed by either specific pharmacological PDE2 inhibition or cardiomyocyte-specific PDE2 deletion. Conclusions: CNP shows strong PDE2-dependent antiarrhythmic effects. Consequently, the CNP-PDE2 axis represents a novel and attractive target for future antiarrhythmic strategies

PTPIP51—A New RelA-tionship with the NFκB Signaling Pathway

The present study shows a new connection of protein tyrosine phosphatase interacting protein 51 (PTPIP51) to the nuclear factor κB (NFκB) signalling pathway. PTPIP51 mRNA and protein expression is regulated by RelA. If bound to the PTPIP51 promoter, RelA repress the mRNA and protein expression of PTPIP51. The parallel treatment with pyrrolidine dithiocarbamate (PDTC) reversed the suppression of PTPIP51 protein expression induced by TNFα. Using the intensity correlation analysis PTPIP51 verified a co-localization with RelA, which is also regulated by TNFα administration. Moreover, the direct interaction of PTPIP51 and RelA was established using the DuoLink proximity ligation assay. IκBα, the known inhibitor of RelA, also interacted with PTPIP51. This hints to the fact that in un-stimulated conditions PTPIP51 forms a complex with RelA and IκBα. The PTPIP51/RelA/IκBα complex is modulated by TNFα. Interestingly, the impact on the mitogen activated protein kinase pathway was negligible except in highest TNFα concentration. Here, PTPIP51 and Raf-1 interactions were slightly repressed. The newly established relationship of PTPIP51 and the NFκB signaling pathway provides the basis for a possible therapeutic impact

Low carb and ketogenic diets increase quality of life, physical performance, body composition, and metabolic health of women with breast cancer

Breast cancer (BC) patients often ask for a healthy diet. Here, we investigated a healthy standard diet (SD), a low carb diet (LCD), and a ketogenic diet (KD) for BC patients during the rehabilitation phase. KOLIBRI was an open-label non-randomized one-site nutritional intervention trial, combining inpatient and outpatient phases for 20 weeks. Female BC patients (n = 152; mean age 51.7 years) could select their diet. Data collected were: Quality of life (QoL), spiroergometry, body composition, and blood parameters. In total 30, 92, and 30 patients started the KD, LCD, and SD, respectively. Of those, 20, 76, and 25 completed the final examination. Patients rated all diets as feasible in daily life. All groups enhanced QoL, body composition, and physical performance. LCD participants showed the most impressive improvement in QoL aspects. KD participants finished with a very good physical performance and muscle/fat ratio. Despite increased cholesterol levels, KD patients had the best triglyceride/high-density lipoprotein (HDL) ratio and homeostatic model assessment of insulin resistance index (HOMA-IR). Most metabolic parameters significantly improved in the LCD group. SD participants ended with remarkably low cholesterol levels but did not improve triglyceride/HDL or HOMA-IR. In conclusion, both well-defined KDs and LCDs are safe and beneficial for BC patients and can be recommended during the rehabilitation phase

Targeting cardiomyocyte ADAM10 ectodomain shedding promotes survival early after myocardial infarction

After myocardial infarction the innate immune response is pivotal in clearing of tissue debris as well as scar formation, but exaggerated cytokine and chemokine secretion with subsequent leukocyte infiltration also leads to further tissue damage. Here, we address the value of targeting a previously unknown a disintegrin and metalloprotease 10 (ADAM10)/CX3CL1 axis in the regulation of neutrophil recruitment early after MI. We show that myocardial ADAM10 is distinctly upregulated in myocardial biopsies from patients with ischemia-driven cardiomyopathy. Intriguingly, upon MI in mice, pharmacological ADAM10 inhibition as well as genetic cardiomycyte-specific ADAM10 deletion improves survival with markedly enhanced heart function and reduced scar size. Mechanistically, abolished ADAM10-mediated CX3CL1 ectodomain shedding leads to diminished IL-1β-dependent inflammation, reduced neutrophil bone marrow egress as well as myocardial tissue infiltration. Thus, our data shows a conceptual insight into how acute MI induces chemotactic signaling via ectodomain shedding in cardiomyocytes