Isomonodromic deformation of resonant rational connections

We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also allowed to be resonant in the sense that the leading coefficient matrix at each singularity may have arbitrary Jordan canonical form, with a genericity condition on the Lidskii submatrix of the subleading term. We also give the relevant notion of isomonodromic tau function extending the one of non-resonant deformations introduced by Miwa-Jimbo-Ueno. The tau function is expressed purely in terms of spectral invariants of the matrix of the connection.Comment: 48 page

Mesoscopic colonization of a spectral band

We consider the unitary matrix model in the limit where the size of the matrices become infinite and in the critical situation when a new spectral band is about to emerge. In previous works the number of expected eigenvalues in a neighborhood of the band was fixed and finite, a situation that was termed "birth of a cut" or "first colonization". We now consider the transitional regime where this microscopic population in the new band grows without bounds but at a slower rate than the size of the matrix. The local population in the new band organizes in a "mesoscopic" regime, in between the macroscopic behavior of the full system and the previously studied microscopic one. The mesoscopic colony may form a finite number of new bands, with a maximum number dictated by the degree of criticality of the original potential. We describe the delicate scaling limit that realizes/controls the mesoscopic colony. The method we use is the steepest descent analysis of the Riemann-Hilbert problem that is satisfied by the associated orthogonal polynomials.Comment: 17 pages, 2 figures, minor corrections and addition

The Hamiltonian Structure of the Second Painleve Hierarchy

In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear ODE of order 2n in the independent variable $z$ depending on n parameters denoted by ${t}_1,...,{t}_{n-1}$ and $\alpha_n$. We introduce new canonical coordinates and obtain Hamiltonians for the $z$ and $t_1,...,t_{n-1}$ evolutions. We give explicit formulae for these Hamiltonians showing that they are polynomials in our canonical coordinates

DPHL: A DIA Pan-human Protein Mass Spectrometry Library for Robust Biomarker Discovery

To address the increasing need for detecting and validating protein biomarkers in clinical specimens, mass spectrometry (MS)-based targeted proteomic techniques, including the selected reaction monitoring (SRM), parallel reaction monitoring (PRM), and massively parallel data-independent acquisition (DIA), have been developed. For optimal performance, they require the fragment ion spectra of targeted peptides as prior knowledge. In this report, we describe a MS pipeline and spectral resource to support targeted proteomics studies for human tissue samples. To build the spectral resource, we integrated common open-source MS computational tools to assemble a freely accessible computational workflow based on Docker. We then applied the workflow to generate DPHL, a comprehensive DIA pan-human library, from 1096 data-dependent acquisition (DDA) MS raw files for 16 types of cancer samples. This extensive spectral resource was then applied to a proteomic study of 17 prostate cancer (PCa) patients. Thereafter, PRM validation was applied to a larger study of 57 PCa patients and the differential expression of three proteins in prostate tumor was validated. As a second application, the DPHL spectral resource was applied to a study consisting of plasma samples from 19 diffuse large B cell lymphoma (DLBCL) patients and 18 healthy control subjects. Differentially expressed proteins between DLBCL patients and healthy control subjects were detected by DIA-MS and confirmed by PRM. These data demonstrate that the DPHL supports DIA and PRM MS pipelines for robust protein biomarker discovery. DPHL is freely accessible at https://www.iprox.org/page/project.html?id=IPX0001400000

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data