Rigid systems of second-order linear differential equations

We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t), u(t)=Udy(t)/dt+Vy(t)+Pv(t) with nonsingular S and P to each system obtained from it by a small enough perturbation of its matrices A,B,C. We prove that there exists a rigid system if and only if m<n(1+square_root{5})/2, and describe all rigid systems.Comment: 22 page

Higher COVID-19 pneumonia risk associated with anti-IFN-α than with anti-IFN-ω auto-Abs in children

We found that 19 (10.4%) of 183 unvaccinated children hospitalized for COVID-19 pneumonia had autoantibodies (auto-Abs) neutralizing type I IFNs (IFN-alpha 2 in 10 patients: IFN-alpha 2 only in three, IFN-alpha 2 plus IFN-omega in five, and IFN-alpha 2, IFN-omega plus IFN-beta in two; IFN-omega only in nine patients). Seven children (3.8%) had Abs neutralizing at least 10 ng/ml of one IFN, whereas the other 12 (6.6%) had Abs neutralizing only 100 pg/ml. The auto-Abs neutralized both unglycosylated and glycosylated IFNs. We also detected auto-Abs neutralizing 100 pg/ml IFN-alpha 2 in 4 of 2,267 uninfected children (0.2%) and auto-Abs neutralizing IFN-omega in 45 children (2%). The odds ratios (ORs) for life-threatening COVID-19 pneumonia were, therefore, higher for auto-Abs neutralizing IFN-alpha 2 only (OR [95% CI] = 67.6 [5.7-9,196.6]) than for auto-Abs neutralizing IFN-. only (OR [95% CI] = 2.6 [1.2-5.3]). ORs were also higher for auto-Abs neutralizing high concentrations (OR [95% CI] = 12.9 [4.6-35.9]) than for those neutralizing low concentrations (OR [95% CI] = 5.5 [3.1-9.6]) of IFN-omega and/or IFN-alpha 2

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 &lt;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

Discovering HIV related information by means of association rules and machine learning

Acquired immunodeficiency syndrome (AIDS) is still one of the main health problems worldwide. It is therefore essential to keep making progress in improving the prognosis and quality of life of affected patients. One way to advance along this pathway is to uncover connections between other disorders associated with HIV/AIDS-so that they can be anticipated and possibly mitigated. We propose to achieve this by using Association Rules (ARs). They allow us to represent the dependencies between a number of diseases and other specific diseases. However, classical techniques systematically generate every AR meeting some minimal conditions on data frequency, hence generating a vast amount of uninteresting ARs, which need to be filtered out. The lack of manually annotated ARs has favored unsupervised filtering, even though they produce limited results. In this paper, we propose a semi-supervised system, able to identify relevant ARs among HIV-related diseases with a minimal amount of annotated training data. Our system has been able to extract a good number of relationships between HIV-related diseases that have been previously detected in the literature but are scattered and are often little known. Furthermore, a number of plausible new relationships have shown up which deserve further investigation by qualified medical experts

Role of PATJ in stroke prognosis by modulating endothelial to mesenchymal transition through the Hippo/Notch/PI3K axis

Abstract Through GWAS studies we identified PATJ associated with functional outcome after ischemic stroke (IS). The aim of this study was to determine PATJ role in brain endothelial cells (ECs) in the context of stroke outcome. PATJ expression analyses in patient’s blood revealed that: (i) the risk allele of rs76221407 induces higher expression of PATJ, (ii) PATJ is downregulated 24 h after IS, and (iii) its expression is significantly lower in those patients with functional independence, measured at 3 months with the modified Rankin scale ((mRS) ≤2), compared to those patients with marked disability (mRS = 4–5). In mice brains, PATJ was also downregulated in the injured hemisphere at 48 h after ischemia. Oxygen-glucose deprivation and hypoxia-dependent of Hypoxia Inducible Factor-1α also caused PATJ depletion in ECs. To study the effects of PATJ downregulation, we generated PATJ-knockdown human microvascular ECs. Their transcriptomic profile evidenced a complex cell reprogramming involving Notch, TGF-ß, PI3K/Akt, and Hippo signaling that translates in morphological and functional changes compatible with endothelial to mesenchymal transition (EndMT). PATJ depletion caused loss of cell-cell adhesion, upregulation of metalloproteases, actin cytoskeleton remodeling, cytoplasmic accumulation of the signal transducer C-terminal transmembrane Mucin 1 (MUC1-C) and downregulation of Notch and Hippo signaling. The EndMT phenotype of PATJ-depleted cells was associated with the nuclear recruitment of MUC1-C, YAP/TAZ, β-catenin, and ZEB1. Our results suggest that PATJ downregulation 24 h after IS promotes EndMT, an initial step prior to secondary activation of a pro-angiogenic program. This effect is associated with functional independence suggesting that activation of EndMT shortly after stroke onset is beneficial for stroke recovery