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

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

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

Quantum toboggans: models exhibiting a multisheeted PT symmetry

A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is described. It uses analytic potentials V(x) (with singularities) and a generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial toboggans are defined as integrated along topologically nontrivial paths of coordinates running over several Riemann sheets of wave functions.Comment: 16 pp, 5 figs. Written version of the talk given during 5th International Symposium on Quantum Theory and Symmetries, University of Valladolid, Spain, July 22 - 28 2007, webpage http://tristan.fam.uva.es/~qts

Levy statistics and anomalous transport in quantum-dot arrays

A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of transmission events and thereby requires no time dependence of system properties. The waiting time distribution with a characteristic long tail gives rise to a nonstationary response in the presence of a voltage pulse. We report on noise measurements that agree well with the predicted non-Poissonian fluctuations in current, and discuss possible mechanisms leading to this behavior.Comment: 7 pages, 2 figure

Bibliografia historii gospodarczej Polski w latach 1944-1989

S\u142owa kluczowe: historia gospodarcza Polski Ludowej; bibliografia prac z lat 1944-2002; biografie i pami\u119tniki; informatory; prasa gospodarcz

Colloidal topological insulators

Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge states in a classical particle system. Magnetic colloidal particles travel along the edge of two distinct magnetic lattices. We drive the colloids with a uniform external magnetic field that performs a topologically non-trivial modulation loop. The loop induces closed orbits in the bulk of the magnetic lattices. At the edge, where both lattices merge, the colloids perform skipping orbits trajectories and hence edge-transport. We also observe paramagnetic and diamagnetic colloids moving in opposite directions along the edge between two inverted patterns; the analogue of a quantum spin Hall effect in topological insulators. We present a new, robust, and versatile way of transporting colloidal particles, enabling new pathways towards lab on a chip applications

Characteristics of drug-resistant tuberculosis in Abkhazia (Georgia), a high-prevalence area in Eastern Europe

Although multidrug-resistant (MDR) tuberculosis (TB) is a major public health problem in Eastern Europe, the factors contributing to emergence, spread and containment of MDR-TB are not well defined. Here, we analysed the characteristics of drug-resistant TB in a cross-sectional study in Abkhazia (Georgia) between 2003 and 2005, where standard short-course chemotherapy is supplemented with individualized drug-resistance therapy. Drug susceptibility testing (DST) and molecular typing were carried out for Mycobacterium tuberculosis complex strains from consecutive smear-positive TB patients. Out of 366 patients, 60.4% were resistant to any first-line drugs and 21% had MDR-TB. Overall, 25% of all strains belong to the Beijing genotype, which was found to be strongly associated with the risk of MDR-TB (OR 25.9, 95% CI 10.2-66.0) and transmission (OR 2.8, 95% CI 1.6-5.0). One dominant MDR Beijing clone represents 23% of all MDR-TB cases. The level of MDR-TB did not decline during the study period, coinciding with increasing levels of MDR Beijing strains among previously treated cases. Standard chemotherapy plus individualized drug-resistance therapy, guided by conventional DST, might be not sufficient to control MDR-TB in Eastern Europe in light of the spread of "highly transmissible" MDR Beijing strains circulating in the community