On a class of generalized solutions to equations describing incompressible viscous fluids

We consider a class of viscous fluids with a general monotone dependence of the viscous stress on the symmetric velocity gradient. We introduce the concept of dissipative solution to the associated initial boundary value problem inspired by the measure-valued solutions for the inviscid (Euler) system. We show the existence as well as the weak-strong uniqueness property in the class of dissipative solutions. Finally, the dissipative solution enjoying certain extra regularity coincides with a strong solution of the same problem

Comprehensive LESA Mass Spectrometry Imaging of Intact Proteins by Integration of Cylindrical FAIMS

The benefits of high field asymmetric waveform ion mobility spectrometry (FAIMS) for mass spectrometry imaging of intact proteins in thin tissue sections have been demonstrated previously. In those works, a planar FAIMS device coupled with a Thermo Elite mass spectrometer was employed. Here, we have evaluated a newly introduced cylindrical FAIMS device (the FAIMS Pro) coupled with a Thermo Fusion Lumos mass spectrometer for liquid extraction surface analysis mass spectrometry imaging of intact proteins in thin tissue sections from rat testes, kidney, and brain. The method makes use of multiple FAIMS compensation values at each location (pixel) of the imaging array. A total of 975 nonredundant protein species were detected in the testes imaging dataset, 981 in the kidney dataset, and 249 in the brain dataset. These numbers represent a 7-fold (brain) and over 10-fold (testes, kidney) improvement on the numbers of proteins previously detected in LESA FAIMS imaging, and a 10-fold to over 20-fold improvement on the numbers detected without FAIMS on this higher performance mass spectrometer, approaching the same order of magnitude as those obtained in top-down proteomics of cell lines. Nevertheless, high throughput identification within the LESA FAIMS imaging workflow remains a challenge

Multi-site assessment of the precision and reproducibility of multiple reaction monitoring–based measurements of proteins in plasma

Verification of candidate biomarkers relies upon specific, quantitative assays optimized for selective detection of target proteins, and is increasingly viewed as a critical step in the discovery pipeline that bridges unbiased biomarker discovery to preclinical validation. Although individual laboratories have demonstrated that multiple reaction monitoring (MRM) coupled with isotope dilution mass spectrometry can quantify candidate protein biomarkers in plasma, reproducibility and transferability of these assays between laboratories have not been demonstrated. We describe a multilaboratory study to assess reproducibility, recovery, linear dynamic range and limits of detection and quantification of multiplexed, MRM-based assays, conducted by NCI-CPTAC. Using common materials and standardized protocols, we demonstrate that these assays can be highly reproducible within and across laboratories and instrument platforms, and are sensitive to low µg/ml protein concentrations in unfractionated plasma. We provide data and benchmarks against which individual laboratories can compare their performance and evaluate new technologies for biomarker verification in plasma

THE OBERBECK–BOUSSINESQ SYSTEM WITH NON-LOCAL BOUNDARY CONDITIONS

We consider the Oberbeck–Boussinesq system with non-local boundary conditions arising as a singular limit of the full Navier–Stokes–Fourier system in the regime of low Mach and low Froude numbers. The existence of strong solutions is shown on a maximal time interval [0, Tmax). Moreover, Tmax = ∞ in the two-dimensional settin

On Strong Continuity of Weak Solutions to the Compressible Euler System

Let S = {tau(n)}(n=1)(infinity) subset of (0, T) be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions that are not strongly continuous at each tau(n) , n=1,2, .... The proof is based on a refined version of the oscillatory lemma of De Lellis and Szekelyhidi with coefficients that may be discontinuous on a set of zero Lebesgue measure

Statistical characterization of multiple-reaction monitoring mass spectrometry (MRM-MS) assays for quantitative proteomics

Multiple reaction monitoring mass spectrometry (MRM-MS) with stable isotope dilution (SID) is increasingly becoming a widely accepted assay for the quantification of proteins and peptides. These assays have shown great promise in relatively high throughput verification of candidate biomarkers. While the use of MRM-MS assays is well established in the small molecule realm, their introduction and use in proteomics is relatively recent. As such, statistical and computational methods for the analysis of MRM-MS data from proteins and peptides are still being developed. Based on our extensive experience with analyzing a wide range of SID-MRM-MS data, we set forth a methodology for analysis that encompasses significant aspects ranging from data quality assessment, assay characterization including calibration curves, limits of detection (LOD) and quantification (LOQ), and measurement of intra- and interlaboratory precision. We draw upon publicly available seminal datasets to illustrate our methods and algorithms.National Cancer Institute (U.S.) (Grant U24CA126476)National Heart, Lung, and Blood Institute (Grant HHSN268201000033C