Constructions of Coupling Processes for L\'evy Processes

We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by reflection.Comment: 16 page

Detecting independence of random vectors: generalized distance covariance and Gaussian covariance

Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Sz\'{e}kely, Rizzo and Bakirov can be embedded into a more general framework based on symmetric L\'{e}vy measures and the corresponding real-valued continuous negative definite functions. The L\'{e}vy measures replace the weight functions used in the original definition of distance covariance. All essential properties of distance covariance are preserved in this new framework. From a practical point of view this allows less restrictive moment conditions on the underlying random variables and one can use other distance functions than Euclidean distance, e.g. Minkowski distance. Most importantly, it serves as the basic building block for distance multivariance, a quantity to measure and estimate dependence of multiple random vectors, which is introduced in a follow-up paper [Distance Multivariance: New dependence measures for random vectors (submitted). Revised version of arXiv: 1711.07775v1] to the present article.Comment: Published at https://doi.org/10.15559/18-VMSTA116 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

Anodic dissolution of aluminum and anodic passivation in [EMIm]Cl-based ionic liquids

The anodic dissolution of aluminum in Lewis acidic ionic liquids consisting of AlCl3 and 1-ethyl-3-methylimidazolium chloride was studied using linear sweep and cyclic voltammetry, an electrochemical quartz crystal microbalance (EQCM) and chronopotentiometry at ambient temperature. Anodic passivation of the working electrode was observed in a 2:1 electrolyte while no passivation was found in a 1.5:1 electrolyte. Chronopotentiometry proves the passivation to be caused by local solidification of the electrolyte due to an increase in the aluminum concentration near the anode. EQCM data support these results

Bestimmung von Werkstoffkennwerten mit Ultraschallverfahren - ist der 'Goldbarren' echt?

Derzeit werden für die vielfältigen Anforderungen in der Technik immer neue Werkstoffe entwickelt. Zur Sicherung einer gleichbleibenden Qualität ist die Bestimmung von mechanischen Werkstoffkennwerten wie Elastizitätsmodul, Gleitmodul, Querkontraktionszahl, aber auch die Gefügebeurteilung, notwendig. Diese Kenngrößen sollten zerstörungsfrei ermittelbar sein. Mit Impulsecho-Ultraschallverfahren in Tauchtechnik und einer speziellen Fourierfilterung der Echosignale lassen sich auch an dünnen Proben mit einer kleinen Stufe mit der vorgestellten Methode diese Kennwerte sicher bestimmen. Gegebenenfalls lassen sich sogar real geformte Bauteile mit einer entsprechenden Stufe untersuchen. Es wird dabei an den Differenzsignalen die Schallgeschwindigkeit bestimmt. Vorteilhaft ist dabei die konstante Ankopplung in Tauchtechnik. Durch die Fourierfilterung lassen sich so Stufen bzw. Schichten ab 200 μm und größer, je nach Schallgeschwindigkeit des Materials, mit hoher Genauigkeit untersuchen. Über die gegebenenfalls mögliche Trennung vom Echo der Vorderseite und der Rückseite des Bleches lässt sich die Schwächung ermitteln und damit sind Aussagen zum Gefüge möglich [1]. Damit lassen sich zerstörende Messungen mit komplizierteren Anforderungen an die Probe, wie beim Zugversuch, stark einschränken. Aber auch über die Messung der Schallgeschwindigkeit Longitudinal oder Transversal nicht in Tauchtechnik lassen sich Fälschungen, wie derzeit an „Goldbarren“ aus Wolfram sicher nachweisen. Die Fälschungen sind nur mit einer dicken, nicht durch Röntgenfluoreszenz durchdringenden Goldschicht plattiert. Die erheblichen Unterschiede in der Schallgeschwindigkeit im Wolfram mit 5261 m/s zum Gold mit 3240 m/s sind zerstörungsfrei sicher messbar und erfassen den gesamten Probenbereich. Die Gesamtdicke muss lediglich zugänglich sein. Es brauchen so bei der Goldbarrenprüfung keine Späne entnommen oder Kerben eingeschlagen werden

Probabilistic graphlets capture biological function in probabilistic molecular networks

Motivation: Molecular interactions have been successfully modeled and analyzed as networks, where nodes represent molecules and edges represent the interactions between them. These networks revealed that molecules with similar local network structure also have similar biological functions. The most sensitive measures of network structure are based on graphlets. However, graphlet-based methods thus far are only applicable to unweighted networks, whereas real-world molecular networks may have weighted edges that can represent the probability of an interaction occurring in the cell. This information is commonly discarded when applying thresholds to generate unweighted networks, which may lead to information loss. Results: We introduce probabilistic graphlets as a tool for analyzing the local wiring patterns of probabilistic networks. To assess their performance compared to unweighted graphlets, we generate synthetic networks based on different well-known random network models and edge probability distributions and demonstrate that probabilistic graphlets outperform their unweighted counterparts in distinguishing network structures. Then we model different real-world molecular interaction networks as weighted graphs with probabilities as weights on edges and we analyze them with our new weighted graphlets-based methods. We show that due to their probabilistic nature, probabilistic graphlet-based methods more robustly capture biological information in these data, while simultaneously showing a higher sensitivity to identify condition-specific functions compared to their unweighted graphlet-based method counterparts.This work was supported by the European Research Council (ERC) Consolidator Grant 770827, the Serbian Ministry of Education and Science. Project III44006, the Slovenian Research Agency project J1-8155 and The Prostate Project.Peer ReviewedPostprint (author's final draft

Gene-expression analysis of gleason grade 3 tumor glands embedded in low- and high-risk prostate cancer

The Gleason score (GS) of prostate cancer on diagnostic biopsies is an important parameter for therapeutic decision-making. Biopsy GS under-estimates the actual GS at radical prostatectomy in a significant number of patients due to sampling artifact. The aim of this study was to identify markers that are differentially expressed in Gleason grade 3 (GG3) tumor glands embedded in GS 4 + 3 = 7 and GS 3 + 3 = 6 prostate cancer using laser capture microdissection and RNA sequencing. GG3 tumor glands embedded in nine GS 3 + 3 = 6 and nine GS 4 + 3 = 7 prostate cancers were isolated by laser capture microdissection of frozen radical prostatectomy specimens. After RNA amplification and RNA sequencing, differentially expressed genes in both GG3 components were identified by a 2log fold change > 1.0 and p-value < 0.05. We applied immunohistochemistry on a tissue micro-array representing 481 radical prostatectomy samples for further validation on protein level. A total of 501 genes were up-regulated and 421 down-regulated in GG3 glands embedded in GS 4 + 3 = 7 as compared to GS 3 + 3 = 6 prostate cancer. We selected HELLS, ZIC2 and ZIC5 genes for further validation. ZIC5 mRNA was up-regulated 17 fold (p = 8.4E–07), ZIC2 8 fold (p = 1.3E–05) and HELLS 2 fold (p = 0.006) in GG3 glands derived from GS 4 + 3 = 7. HELLS expression of ≥ 1% occurred in 10% GS < 7, 17% GS 7 and 43% GS >7 prostate cancer (p < 0.001). Using a cut-off of ≥ 1%, protein expression of ZIC5 was present in 28% GS 7 cancer (p < 0.001). ZIC2 was neither associated with GS nor outcome in our validation set. HELLS was independently predictive for biochemical-recurrence after radical prostatectomy (HR 2.3; CI 1.5–3.6; p < 0.01). In conclusion, HELLS and ZIC5 might be promising candidate markers for selection of biopsy GS 6 prostate cancer being at risk for up-grading at prostatectomy

Multi-parameter immune profiling of peripheral blood mononuclear cells by multiplexed single-cell mass cytometry in patients with early multiple sclerosis

Multiple sclerosis (MS) is an inflammatory demyelinating and neurodegenerative disease of the central nervous system (CNS). Studies in rodent models demonstrated an association of CNS-infiltrating monocyte-derived macrophages with disease severity. However, little is known about humans. Here, we performed an exploratory analysis of peripheral blood mononuclear cells (PBMCs) isolated from healthy controls and drug-naïve patients with early MS using multiplexed single-cell mass cytometry and algorithm-based data analysis. Two antibody panels comprising a total of 64 antibodies were designed to comprehensively analyse diverse immune cell populations, with particular emphasis on monocytes. PBMC composition and marker expression were overall similar between the groups. However, an increased abundance of CCR7+ and IL-6+ T cells was detected in early MS-PBMCs, whereas NFAT1hiT-bethiCD4+ T cells were decreased. Similarly, we detected changes in the subset composition of the CCR7+ and MIPβhi HLA-DR+ lymphocyte compartment. Only mild alterations were detected in monocytes/myeloid cells of patients with early MS, namely a decreased abundance of CD141hiIRF8hiCXCR3+CD68- dendritic cells. Unlike in Crohn's disease, no significant differences were found in the monocyte fraction of patients with early MS compared to healthy controls. This study provides a valuable resource for future studies designed to characterise and target diverse PBMC subsets in MS