Limiting behavior of the eigenvalues of a multivariate F matrix

AbstractThe spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity

Spectrum of non-Hermitian heavy tailed random matrices

Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some additional smoothness assumptions on the law of X_{jk}, we prove that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability measure mu_alpha on C depending only on alpha such that with probability one, the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1} (X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our approach combines Aldous & Steele's objective method with Girko's Hermitization using logarithmic potentials. The underlying limiting object is defined on a bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive relations on the tree provide some properties of mu_alpha. In contrast with the Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in Mathematical Physics 307, 513-560 (2011

Circular Law Theorem for Random Markov Matrices

Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d. rows obtained from X by dividing each row of X by its sum. In particular, when X11 follows an exponential law, then M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Our main result states that with probability one, the counting probability measure of the complex spectrum of n^(1/2)M converges weakly as n tends to infinity to the uniform law on the centered disk of radius sigma/m. The bounded density assumption is purely technical and comes from the way we control the operator norm of the resolvent.Comment: technical update via http://HAL.archives-ouvertes.f

Genome-wide association meta-analyses and fine-mapping elucidate pathways influencing albuminuria

Publisher Copyright: © 2019, The Author(s).Increased levels of the urinary albumin-to-creatinine ratio (UACR) are associated with higher risk of kidney disease progression and cardiovascular events, but underlying mechanisms are incompletely understood. Here, we conduct trans-ethnic (n = 564,257) and European-ancestry specific meta-analyses of genome-wide association studies of UACR, including ancestry- and diabetes-specific analyses, and identify 68 UACR-associated loci. Genetic correlation analyses and risk score associations in an independent electronic medical records database (n = 192,868) reveal connections with proteinuria, hyperlipidemia, gout, and hypertension. Fine-mapping and trans-Omics analyses with gene expression in 47 tissues and plasma protein levels implicate genes potentially operating through differential expression in kidney (including TGFB1, MUC1, PRKCI, and OAF), and allow coupling of UACR associations to altered plasma OAF concentrations. Knockdown of OAF and PRKCI orthologs in Drosophila nephrocytes reduces albumin endocytosis. Silencing fly PRKCI further impairs slit diaphragm formation. These results generate a priority list of genes and pathways for translational research to reduce albuminuria.Peer reviewe

Dynamic analysis and field investigation of a fluidized landslide in Guanling, Guizhou, China

On June 28, 2010, a large catastrophic landslide was triggered by a heavy rainfall in Guanling, Guizhou, China. This catastrophic event destroyed two villages and caused 99 casualties. The landslide involved the failure of about 985, 000 m[3] of sandstone from the source area. The displaced materials traveled about 1300 m with a descent of about 400 m, covering an area of 129, 000 m2 with the final volume being accumulated to be 1, 840, 000 m[3], approximately. To provide information for hazard zonation of similar type of landslides in the same area, we used a dynamic model (DAN3D) to simulate the runout behavior of the displaced landslide materials, and found that a combined frictional–Vollemy model could provide the best performance in simulating this landslide and the runout is precisely duplicated with a dynamic friction angle (ϕ) of 30° and a pore pressure ratio (ru) of 0.55 for the materials at the source area and with Vollemy parameters of friction coefficient f = 0.1 (dimensionless) and turbulent coefficient ξ = 400 m/s[2]. The simulated results indicated that the duration of the movement is estimated at about 60 s for a mean velocity 23 m/s. To examine the effectiveness of simulation by means of DAN3D and also to evaluate the reactivation potential of these displaced landslide materials depositing on the valley, we used electrical resistivity tomography (ERT) method to survey the depth and internal structure of landslide deposits. The ERT results showed that DAN3D gave a good prediction on the shape and runout distance of the landslide deposits, although the predicted maximum depths of landslide deposit on some areas were differing from those obtained by ERT method