Lyapunov exponents for products of complex Gaussian random matrices

The exact value of the Lyapunov exponents for the random matrix product $P_N = A_N A_{N-1}...A_1$ with each $A_i = \Sigma^{1/2} G_i^{\rm c}$, where $\Sigma$ is a fixed $d \times d$ positive definite matrix and $G_i^{\rm c}$ a $d \times d$ complex Gaussian matrix with entries standard complex normals, are calculated. Also obtained is an exact expression for the sum of the Lyapunov exponents in both the complex and real cases, and the Lyapunov exponents for diffusing complex matrices.Comment: 15 page

Autoantibodies against type I IFNs in patients with life-threatening COVID-19

Interindividual clinical variability in the course of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is vast. We report that at least 101 of 987 patients with life-threatening coronavirus disease 2019 (COVID-19) pneumonia had neutralizing immunoglobulin G (IgG) autoantibodies (auto-Abs) against interferon-w (IFN-w) (13 patients), against the 13 types of IFN-a (36), or against both (52) at the onset of critical disease; a few also had auto-Abs against the other three type I IFNs. The auto-Abs neutralize the ability of the corresponding type I IFNs to block SARS-CoV-2 infection in vitro. These auto-Abs were not found in 663 individuals with asymptomatic or mild SARS-CoV-2 infection and were present in only 4 of 1227 healthy individuals. Patients with auto-Abs were aged 25 to 87 years and 95 of the 101 were men. A B cell autoimmune phenocopy of inborn errors of type I IFN immunity accounts for life-threatening COVID-19 pneumonia in at least 2.6% of women and 12.5% of men

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Prognostic models to predict survival in indolent and aggressive Non-Hodgkin's lymphomas associated with hepatitis C virus infection : a multicenter Italian study on 1,043 patients

Epidemiological studies demonstrated that HCV is associated with B-cell NHL. A precise prognostication of HCV+ NHL is not available; in particular, the impact of liver toxicity on the outcome of pts treated with (immuno)-chemotherapy is not fully clarified. Aim of the present study was to analyse clinical and virological characteristics, toxicity and prognosis of a large series of indolent and aggressive HCV+ NHL. We studied 1,043 pts with HCV+ NHL diagnosed and treated from January 1993 to December 2009 in 15 italian hematologic institutions; 539 cases were aggressive NHL (522 DLBCL) and 504 indolent NHL (265 MZL). All pts were HIV negative, 3% carried HBsAg and 91% were HCV-RNA+. Thirteen out of 56 HCV-RNA negative pts cleared HCV by means of antiviral therapy before NHL diagnosis. An (immuno)-chemotherapy regimen was administered as first-line treatment in 859 pts: 537 received CHOP-like regimen (+ Rituximab 243), 66 III generation regimen, 174 alkylators, 30 purine analogues, 31 other regimens, 21 R alone. Doses of chemotherapy since first cycle were reduced in 31% of pts. A watch-and-wait policy was adopted in 82 pts, other treatments in 68 pts and anti-HCV antiviral therapy in 34 pts with indolent NHL (12 of whom obtained both a complete virologic and hematologic response). Hepatic toxicity was evaluable in 597 patients: among 347 pts with normal ALT at NHL diagnosis, 52 (15%) developed WHO hepatic toxicity grade 2; among 250 pts (42%) with abnormal ALT, 26 (11%) experienced ALT increase >3.5 times baseline value. Overall, a significant liver toxicity developed in 78 pts (13%) (15% of aggressive NHL and 10% of indolent NHL). Use of Rituximab was not associated with significant liver toxicity (p=0.4); particularly, in DLBCL, R-CHOP and CHOP showed the same rate of significant hepatic toxicity (15%, p=ns), although maximum grade of liver toxicity was registered earlier in patients treated with R-CHOP than in those treated with CHOP (before 3rd cycle respectively in 57% vs 41%, p=0.006). Planned treatment was not completed in 134 pts (29 for liver toxicity). After a median F-UP of 2.6 years, 321 pts died (24 for liver failure). 5-yrs OS was 76% for indolent NHL and 62% for DLBCL. In indolent NHL, the parameters associated with a shorter OS in univariate analysis were: elevated LDH (p 60 yrs (p106 UI/ml (p 60 yrs (HR 2.11, p=0.02), AA stage III-IV (HR 2.0, p=0.04), no antiviral therapy at any time (HR 2.56, p=0.01). In DLBCL, the parameters associated with a shorter OS in univariate analysis were: elevated LDH (p 60 yrs (p=0.003), liver involvement by lymphoma (p=0.02), B symptoms (p1.7 (p=0.01), Child score (p106 UI/ml (p9 and/or fibrosis stage >2 at liver biopsy (p=0.03). Moreover IPI, aaIPI and R-IPI were predictive for OS (p106 UI/ml (HR 3.59, p=0.001), serum albumin <3.5 g/dl (HR 2.53, p=0.01), while other IPI factors (age, AA stage, LDH, extranodal sites) were excluded from the final model. We combined the 3 factors significantly associated to a worse OS (ECOG, albumin, HCV-RNA load) in a new HCV Prognostic Score (HPS) able to discriminate 3 categories of risk (low=0; intermediate=1; high risk 2 factors) (p<0.001) (Fig. 1). After adjusting by IPI in multivariate Cox regression analysis, the HPS retained prognostic effect (p<0.001), while IPI itself did not. In conclusion, a significant proportion of pts with HCV+ NHL, when treated with conventional (immuno)-chemotherapy, develops severe liver toxicity. In indolent NHL, employment of antiviral therapy at any time during lymphoma history ameliorates OS. In HCV+ DLBCL, addition of rituximab to CHOP scheme does not increase hepatic toxicity; moreover, the new score HPS performs better than IPI in discriminating different risk categories