Classes of generalized functions with finite type regularities

We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities

Novel biomarker SARIFA in colorectal cancer: highly prognostic, not genetically driven and histologic indicator of a distinct tumor biology

SARIFA (Stroma AReactive Invasion Front Areas) has recently emerged as a promising histopathological biomarker for colon and gastric cancer. To elucidate the underlying tumor biology, we assessed SARIFA-status in tissue specimens from The-Cancer-Genome-Atlas (TCGA) cohorts COAD (colonic adenocarcinoma) and READ (rectal adenocarcinoma). For the final analysis, 207 CRC patients could be included, consisting of 69 SARIFA-positive and 138 SARIFA-negative cases. In this external validation cohort, H&E-based SARIFA-positivity was strongly correlated with unfavorable overall, disease-specific, and progression-free survival, partly outperforming conventional prognostic factors. SARIFA-positivity was not associated with known high-risk genetic profiles, such as BRAF V600E mutations or microsatellite-stable status. Transcriptionally, SARIFA-positive CRCs exhibited an overlap with CRC consensus molecular subtypes CMS1 and CMS4, along with distinct differential gene expression patterns, linked to lipid metabolism and increased stromal cell infiltration scores (SIIS). Gene-expression-based drug sensitivity prediction revealed a differential treatment response in SARIFA-positive CRCs. In conclusion, SARIFA represents the H&E-based counterpart of an aggressive tumor biology, demonstrating a partial overlap with CMS1/4 and also adding a further biological layer related to lipid metabolism. Our findings underscore SARIFA-status as an ideal biomarker for refined patient stratification and novel drug developments, particularly given its cost-effective assessment based on routinely available H&E slides

Generalized Fourier Integral Operators on spaces of Colombeau type

Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data

Distributional sources for black hole initial data

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.Comment: Code available at https://github.com/SwampWalker/LeapingMonke

Dynamical extensions for shell-crossing singularities

We derive global weak solutions of Einstein's equations for spherically symmetric dust-filled space-times which admit shell-crossing singularities. In the marginally bound case, the solutions are weak solutions of a conservation law. In the non-marginally bound case, the equations are solved in a generalized sense involving metric functions of bounded variation. The solutions are not unique to the future of the shell-crossing singularity, which is replaced by a shock wave in the present treatment; the metric is bounded but not continuous.Comment: 14 pages, 1 figur

Optimizing end-labeled free-solution electrophoresis by increasing the hydrodynamic friction of the drag-tag

We study the electrophoretic separation of polyelectrolytes of varying lengths by means of end-labeled free-solution electrophoresis (ELFSE). A coarse-grained molecular dynamics simulation model, using full electrostatic interactions and a mesoscopic Lattice Boltzmann fluid to account for hydrodynamic interactions, is used to characterize the drag coefficients of different label types: linear and branched polymeric labels, as well as transiently bound micelles. It is specifically shown that the label's drag coefficient is determined by its hydrodynamic size, and that the drag per label monomer is largest for linear labels. However, the addition of side chains to a linear label offers the possibility to increase the hydrodynamic size, and therefore the label efficiency, without having to increase the linear length of the label, thereby simplifying synthesis. The third class of labels investigated, transiently bound micelles, seems very promising for the usage in ELFSE, as they provide a significant higher hydrodynamic drag than the other label types. The results are compared to theoretical predictions, and we investigate how the efficiency of the ELFSE method can be improved by using smartly designed drag-tags.Comment: 32 pages, 11 figures, submitted to Macromolecule

Transcriptomic Comparison of Human Peripartum and Dilated Cardiomyopathy Identifies Differences in Key Disease Pathways

Peripartum cardiomyopathy (PPCM) is a rare form of acute onset heart failure that presents in otherwise healthy pregnant women around the time of delivery. While most of these women respond to early intervention, about 20% progress to end-stage heart failure that symptomatically resembles dilated cardiomyopathy (DCM). In this study, we examined two independent RNAseq datasets from the left ventricle of end-stage PPCM patients and compared gene expression profiles to female DCM and non-failing donors. Differential gene expression, enrichment analysis and cellular deconvolution were performed to identify key processes in disease pathology. PPCM and DCM display similar enrichment in metabolic pathways and extracellular matrix remodeling suggesting these are similar processes across end-stage systolic heart failure. Genes involved in golgi vesicles biogenesis and budding were enriched in PPCM left ventricles compared to healthy donors but were not found in DCM. Furthermore, changes in immune cell populations are evident in PPCM but to a lesser extent compared to DCM, where the latter is associated with pronounced pro-inflammatory and cytotoxic T cell activity. This study reveals several pathways that are common to end-stage heart failure but also identifies potential targets of disease that may be unique to PPCM and DCM.</p

Thrombosis Is Reduced by Inhibition of COX-1, but Unaffected by Inhibition of COX-2, in an Acute Model of Platelet Activation in the Mouse

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Multi-sensor electromagnetic inspection feasibility for aerospace composites surface defects

UK's presence at the forefront of composite manufacturing in Europe has never been more important provided how vital these structures are for i) slowing the climate change through reduction of fuel consumption and carbon footprint in different industries, and ii) development of wind and tidal blades to generate cleaner energy to achieve the net-zero target by the middle of the century. Therefore, the composite technology, Carbon Fibre Reinforced Polymers (CFRP) in particular, has been dominating the aerospace, energy, and defense industries, and this trend is expected to grow in the years to come. Non-Destructive Evaluation (NDE) is essential during manufacturing: to identify any defects early in the process as, if defects remain undetected, they could have far-reaching implications for the cost of scraped/repaired parts and the safety of final components, and ii) at later stages of manufacturing and post-manufacturing: to ensure the quality, integrity, and fitness for service of these safetycritical components. Although Ultrasound Testing (UT) has been predominantly used for inspection CFRPs owing to its excellent performance for bulk NDE inspections, the method is not sufficiently sensitive to all defect types occurring in such components. Ultrasonic waves transmitted using array probes on CFRP components mainly interact with defects that are extended perpendicularly to the direction of the wave propagation such as delamination. The technique does not offer sufficient sensitivity for the detection of shallow and narrow surface defects commonly created by matrix transversal cracking and barely visible impact damage mechanisms. The compound CFRP gives rise to the mixed electromagnetic properties where highly conductive carbon fibres are molded in a dielectric resin matrix. This provides a unique opportunity to explore the potential of electromagnetic NDE sensing modalities such as Eddy Currents (EC) and electrical Capacitance Imaging (CI) for inspection of surface defects. Accordingly, this feasibility study was aimed at investigating the design, automated robotic delivery, and performance assessment of different sensor technologies for the detection of surface defects through experiments. To this end, machined surface defects were fabricated in a CFRP sample. The automated robotic inspection was implemented for all UT, EC, and CI sensors individually where a novel sensor-enabled robotic system based on a real-time embedded controller was developed. The system components consisting of a KUKA robotic arm, Force/Torque (F/T) sensor, and NDE sensor and controller were interfaced through a core program in LabVIEW enabling a) real-time communication between different hardware, b) data acquisition from all sensors and c) full control of the processes within the cell. Moreover, real-time robot motion corrections driven by the F/T sensor feedback were established to adjust the contact force and orientation of the sensors to the component surface during the scan. All sensors, including the UT roller-probe, EC array, and CI sensor boards, were robotically delivered on the designated surface notches with varying depths of 0.1, 0.2, 0.5, and 5 mm. The results of EC and CI testing showed enhanced detectability with high SNR for the defects shallower than 0.2 mm when compared to the UT B-scan images