Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices (The Extended Version)

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These densities are encoded in the form of the so called M-transforms, for which polynomial equations are found. We exploit the methods of planar diagrammatics, enhanced to the non-Hermitian case, and free random variables, respectively; both are described in the appendices. As particular results of these two main equations, we find the singular behavior of the spectral densities near zero. Moreover, we propose a finite-size form of the spectral density of the product close to the border of its eigenvalues' domain. Also, led by the striking similarity between the two main equations, we put forward a conjecture about a simple relationship between the eigenvalues and singular values of any non-Hermitian random matrix whose spectrum exhibits rotational symmetry around zero.Comment: 50 pages, 8 figures, to appear in the Proceedings of the 23rd Marian Smoluchowski Symposium on Statistical Physics: "Random Matrices, Statistical Physics and Information Theory," September 26-30, 2010, Krakow, Polan

Signal and Noise in Correlation Matrix

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar

Obstructive sleep apnea severity is directly related to suicidal ideation in posttraumatic stress disorder

Posttraumatic stress disorder (PTSD) is associated with suicidal ideation (SI) and obstructive sleep apnea (OSA). There are no studies of OSA diagnosed by sleep study and SI in patients with PTSD. Methods: Forty consenting civilians with PTSD (38 female, mean ±standard deviation age: 44.60 ±12.73) underwent a Level 3 home sleep apnea test (WatchPAT200; Itamar Medical, Israel). OSA severity was measured with the respiratory disturbance index (RDI) (number of apneas, hypopneas and respiratory effort related arousals per hour). SI was measured with Items 9, 35, 39, and 50 of the Brief Symptom Inventory (BSI). Other patient-rated measures included the Beck Depression Inventory, second edition (BDI-II), PTSD Checklist for DSM-5 (PCL-5), and the Pittsburgh Sleep Quality Index PTSD Addendum modified to include only Items 1c, 1e, 1f, and 1g that address nightmares. Results: The RDI (r = .757, P \u3c .001) and oxygen desaturation index (r = .633, P \u3c .001) were directly correlated to SI. Multiple regression analysis using SI as the dependent variable and patient-rated measures as independent variables revealed only RDI (β = .480, t = 4.167, P \u3c .001) and BDI-II (β = .469, t = 3.375, P = .002) as predictors of SI, with adjusted R2 = 0.718. In patients with RDI \u3c 30 events/h (n = 37) correlation of SI with RDI (r = .511, P = .001) but not ODI (r = .312, P = .060) remained significant. Multiple regression analysis (when RDI \u3c 30 events/h) revealed only BDI-II (β = .603, t = 3.492, P = .002), and not RDI (β = .247, t = 1.723, P = .096) as a significant predictor of SI. Conclusions: OSA severity in PTSD was directly related to SI. Depression was a significant mediator in the relationship between RDI and SI, with OSA-related intermittent hypoxemia possibly contributing to this relationship only in severe OSA

Fibroblast Growth Factor 22 Is Not Essential for Skin Development and Repair but Plays a Role in Tumorigenesis

PMCID: PMC3380851This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Utilisation of InSAR for Monitoring of Subsidence over Mining Caving Zones

The utilisation of InSAR techniques for the monitoring of subsidence over mining areas, employing open pit and underground mining methods, has a large potential due to inaccessibility and safety issues associated with the usage of classical surveying techniques. InSAR can also be very competitive concerning the cost of provided results. However, there are a few issues that may significantly limit InSAR applicability for subsidence monitoring in mining areas. The highly dynamic character of subsidence induced by mining, especially employing caving as a mining system, may lead to ambiguity issues. This could happen when the vertical movement between the neighbouring cells (pixels) of the SAR image is greater than quarter of the wavelength of a radar signal over the period between image acquisitions. The altered terrain topography, involving steep slopes and deep pits, may also lead to radar signal layover issues for specific satellite and pit slope geometry.In this paper the authors analyse the above-mentioned issues and present how the InSAR technology was applied as a help to monitor large scale and highly dynamic subsidence for a real case study in Western Australia. It was recognised that the analysis of ground deformation dynamics, based on topographical surveys, may provide a basis for the resolution of ambiguity issues existing in InSAR processing. Also, the new technique involving generation of a detailed DEM based on the current topographical surveys and pixel-by-pixel analysis were applied in order to identify a precise extent of layover areas

Transport properties of annealed CdSe nanocrystal solids

Transport properties of artificial solids composed of colloidal CdSe nanocrystals (NCs) are studied from 6 K to 250 K, before and after annealing. Annealing results in greatly enhanced dark and photocurrent in NC solids, while transmission electron microscopy (TEM) micrographs show that the inter-dot separation decreases. The increased current can be attributed to the enhancement of inter-dot tunneling caused by the decreased separation between NCs and by chemical changes in their organic cap. In addition, the absorption spectra of annealed solids are slightly red-shifted and broadened. These red-shifts may result from the change of the dielectric environment around the NCs. Our measurements also indicate that Coulomb interactions between charges on neighboring NCs play an important role in the tunneling current.Comment: 24 pages,4 figures, 1 tabl

Imaging the charge transport in arrays of CdSe nanocrystals

A novel method to image charge is used to measure the diffusion coefficient of electrons in films of CdSe nanocrystals at room temperature. This method makes possible the study of charge transport in films exhibiting high resistances or very small diffusion coefficients.Comment: 4 pages, 4 jpg figure

Application and effectiveness of respiratory physiotherapy in the prevention and treatment of patients with Covid-19

Introduction: COVID-19 as a respiratory disease is the latest challenge in modern medicine. As in most health problems, respiratory rehabilitation also finds application in this case. Materials and methods: Analysis of available literature, articles in the Google Scholar and PubMed database using keywords: COVID-19, respiratory physiotherapy, lung disease, prevention, therapy. The available literature was subjectively selected, and then the latest version of each article was used. Results: There are many physiotherapeutic methods and techniques that can be applied in the fight against COVID-19 disease, but there is still a lack of scientific research that would confirm their effectiveness in this particular disease entity. Rehabilitation of sick people, both in severe and moderate condition, should be based on airway clearance, respiratory control and adequate physical activity. Conclusions: The issue of rehabilitation in COVID-19 disease requires further interest of researchers because there is still insufficient literature on this subject. Undeniably physiotherapy should be a significant part of the interdisciplinary approach to fight this disease entity, because the effects of its absence can significantly affect the health of patients