Spectral Invariance of Non-Smooth Pseudodifferential Operators

In this paper we discuss some spectral invariance results for non-smooth pseudodifferential operators with coefficients in H\"older spaces. In analogy to the proof in the smooth case of Beals and Ueberberg, we use the characterization of non-smooth pseudodifferential operators to get such a result. The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols and the fact, that in general the composition of two non-smooth pseudodifferential operators is not a pseudodifferential operator. In order to improve these spectral invariance results for certain subsets of non-smooth pseudodifferential operators with coefficients in H\"older spaces, we improve the characterization of non-smooth pseudodifferential operators in a previous work by the authors.Comment: 43 page

Compactness properties for modulation spaces

We prove that if $\omega _1$ and $\omega _2$ are moderate weights and \mascB is a suitable (quasi-)Banach function space, then a necessary and sufficient condition for the embedding i\, :\, M (\omega _1,\mascB )\to M (\omega _2,\mascB ) between two modulation spaces to be compact is that the quotient $\omega _2/\omega _1$ vanishes at infinity. Moreover we show, that the boundedness of $\omega _2/\omega _1$ a necessary and sufficient condition for the previous embedding to be continuous.Comment: 25 page

Spectral Invariance of Quasi-Banach Algebras for Matrices and Pseudodifferential Operators

In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory and data compression problems.Comment: 27 pages. This is the very first version. Some changes are expected to be performed in the next versio

A proteomics sample metadata representation for multiomics integration and big data analysis

The amount of public proteomics data is rapidly increasing but there is no standardized format to describe the sample metadata and their relationship with the dataset files in a way that fully supports their understanding or reanalysis. Here we propose to develop the transcriptomics data format MAGE-TAB into a standard representation for proteomics sample metadata. We implement MAGE-TAB-Proteomics in a crowdsourcing project to manually curate over 200 public datasets. We also describe tools and libraries to validate and submit sample metadata-related information to the PRIDE repository. We expect that these developments will improve the reproducibility and facilitate the reanalysis and integration of public proteomics datasets.publishedVersio

Idiopathic pulmonary arterial hypertension phenotypes determined by cluster analysis from the COMPERA registry

Funding Information: Marius M. Hoeper has received fees for lectures and/or consultations from Acceleron, Actelion, Bayer, MSD, and Pfizer. Nicola Benjamin has received fees for lectures and/or consultations from Actelion. Ekkehard Grünig has received fees for lectures and/or consultations from Actelion, Bayer, GSK, MSD, United Therapeutics, and Pfizer. Karen M. Olsson has received fees for lectures and/or consultations from Actelion, Bayer, United Therapeutics, GSK, and Pfizer. C. Dario Vizza has received fees from Actelion, Bayer, GSK, MSD, Pfizer, and United Therapeutics Europe. Anton Vonk-Noordegraaf has received fees for lectures and/or consultation from Actelion, Bayer, GSK, and MSD. Oliver Distler has/had a consultancy relationship with and/or has received research funding from 4-D Science, Actelion, Active Biotec, Bayer, Biogen Idec, Boehringer Ingelheim Pharma, BMS, ChemoAb, EpiPharm, Ergonex, espeRare foundation, GSK, Genentech/Roche, Inventiva, Lilly, medac, MedImmune, Mitsubishi Tanabe, Pharmacyclics, Pfizer, Sanofi, Serodapharm, and Sinoxa in the area of potential treatments of scleroderma and its complications including pulmonary arterial hypertension. In addition, Prof Distler has a patent for mir-29 for the treatment of systemic sclerosis licensed. Christian Opitz has received fees from Actelion, Bayer, GSK, Pfizer, and Novartis. J. Simon R. Gibbs has received fees for lectures and/or consultations from Actelion, Bayer, Bellerophon, GSK, MSD, and Pfizer. Marion Delcroix has received fees from Actelion, Bayer, GSK, and MSD. H. Ardeschir Ghofrani has received fees from Actelion, Bayer, Gilead, GSK, MSD, Pfizer, and United Therapeutics. Doerte Huscher has received fees for lectures and consultations from Actelion. David Pittrow has received fees for consultations from Actelion, Biogen, Aspen, Bayer, Boehringer Ingelheim, Daiichi Sankyo, and Sanofi. Stephan Rosenkranz has received fees for lectures and/or consultations from Actelion, Bayer, GSK, Pfizer, Novartis, Gilead, MSD, and United Therapeutics. Martin Claussen reports honoraria for lectures from Boehringer Ingelheim Pharma GmbH and Roche Pharma and for serving on advisory boards from Boehringer Ingelheim, outside the submitted work. Heinrike Wilkens reports personal fees from Boehringer and Roche during the conduct of the study and personal fees from Bayer, Biotest, Actelion, GSK, and Pfizer outside the submitted work. Juergen Behr received grants from Boehringer Ingelheim and personal fees for consultation or lectures from Actelion, Bayer, Boehringer Ingelheim, and Roche. Hubert Wirtz reports personal fees from Boehringer Ingelheim and Roche outside the submitted work. Hening Gall reports personal fees from Actelion, AstraZeneca, Bayer, BMS, GSK, Janssen-Cilag, Lilly, MSD, Novartis, OMT, Pfizer, and United Therapeutics outside the submitted work. Elena Pfeuffer-Jovic reports personal fees from Actelion, Boehringer Ingelheim, Novartis, and OMT outside the submitted work. Laura Scelsi reports personal fees from Actelion, Bayer, and MSD outside the submitted work. Siliva Ulrich reports grants from Swiss National Science Foundation, Zurich Lung, Swiss Lung, and Orpha Swiss, and grants and personal fees from Actelion SA/Johnson & Johnson Switzerland and MSD Switzerland outside the submitted work. The remaining authors have no conflicts of interest to disclose. Funding Information: This work was supported by the German Centre of Lung Research (DZL). COMPERA is funded by unrestricted grants from Acceleron , Actelion Pharmaceuticals , Bayer , OMT , and GSK . These companies were not involved in data analysis or the writing of this manuscript. Publisher Copyright: © 2020 The Authors Copyright: Copyright 2020 Elsevier B.V., All rights reserved.The term idiopathic pulmonary arterial hypertension (IPAH) is used to categorize patients with pre-capillary pulmonary hypertension of unknown origin. There is considerable variability in the clinical presentation of these patients. Using data from the Comparative, Prospective Registry of Newly Initiated Therapies for Pulmonary Hypertension, we performed a cluster analysis of 841 patients with IPAH based on age, sex, diffusion capacity of the lung for carbon monoxide (DLCO; <45% vs ≥45% predicted), smoking status, and presence of comorbidities (obesity, hypertension, coronary heart disease, and diabetes mellitus). A hierarchical agglomerative clustering algorithm was performed using Ward's minimum variance method. The clusters were analyzed in terms of baseline characteristics; survival; and response to pulmonary arterial hypertension (PAH) therapy, expressed as changes from baseline to follow-up in functional class, 6-minute walking distance, cardiac biomarkers, and risk. Three clusters were identified: Cluster 1 (n = 106; 12.6%): median age 45 years, 76% females, no comorbidities, mostly never smokers, DLCO ≥45%; Cluster 2 (n = 301; 35.8%): median age 75 years, 98% females, frequent comorbidities, no smoking history, DLCO mostly ≥45%; and Cluster 3 (n = 434; 51.6%): median age 72 years, 72% males, frequent comorbidities, history of smoking, and low DLCO. Patients in Cluster 1 had a better response to PAH treatment than patients in the 2 other clusters. Survival over 5 years was 84.6% in Cluster 1, 59.2% in Cluster 2, and 42.2% in Cluster 3 (unadjusted p < 0.001 for comparison between all groups). The population of patients diagnosed with IPAH is heterogenous. This cluster analysis identified distinct phenotypes, which differed in clinical presentation, response to therapy, and survival.publishersversionPeer reviewe

Characterization of non-smooth pseudodifferential operators

In the last decades the theory of pseudodifferential operators was established as an auxiliary tool for solving problems in the field of partial differential equations. However, proving that the inverse of a partial differential operator is a pseudodifferential operator is often difficult. In order to simplify this task, R. Beals and J. Ueberberg developed a characterization of pseudodifferential operators with smooth symbols. In applications also non-smooth pseudodifferential operators occur. Hence such a characterization would be useful for non-smooth pseudodifferential operators, too. Therefore, we show that every linear operator P, which satisfies some specific continuity assumptions, is a non-smooth pseudo-differential operator whose coefficients are in a Hölder space. With the characterization of non-smooth pseudodifferential operators at hand, we are in the position to verify under suitable conditions the following result: the Lebesgue-spectrum of a non-smooth pseudodifferential operator P, whose coefficient is in a Hölder space, is independent of the chosen Lebesgue Space. With P being continuously invertible as a linear operator on certain Bessel potential spaces, the inverse of P is a non-smooth pseudodifferential operator of the same symbol-class under suitable conditions. In order to reach these goals we make use of the central ideas of the analogous results from R. Beals and J. Ueberberg in the smooth case. The main new difficulties are the limited mapping properties of pseudodifferential operators with non-smooth symbols