Statistics of level spacing of geometric resonances in random binary composites

We study the statistics of level spacing of geometric resonances in the disordered binary networks. For a definite concentration $p$ within the interval $[0.2,0.7]$, numerical calculations indicate that the unfolded level spacing distribution $P(t)$ and level number variance $\Sigma^2(L)$ have the general features. It is also shown that the short-range fluctuation $P(t)$ and long-range spectral correlation $\Sigma^2(L)$ lie between the profiles of the Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation threshold $p_c$, crossover behavior of functions $P(t)$ and $$ is obtained, giving the finite size scaling of mean level spacing $\delta$ and mean level number $n$, which obey the scaling laws, $$ and $n=0.911L^{1.970}$.Comment: 11 pages, 7 figures,submitted to Phys. Rev.

Fluctuations and scaling of inverse participation ratios in random binary resonant composites

We study the statistics of local field distribution solved by the Green's-function formalism (GFF) [Y. Gu et al., Phys. Rev. B {\bf 59} 12847 (1999)] in the disordered binary resonant composites. For a percolating network, the inverse participation ratios (IPR) with $q=2$ are illustrated, as well as the typical local field distributions of localized and extended states. Numerical calculations indicate that for a definite fraction $p$ the distribution function of IPR $P_q$ has a scale invariant form. It is also shown the scaling behavior of the ensemble averaged $$ described by the fractal dimension $D_q$. To relate the eigenvectors correlations to resonance level statistics, the axial symmetry between $D_2$ and the spectral compressibility $\chi$ is obtained.Comment: 7 pages, 6 figures, accepted by Physical Review

One-parameter Superscaling at the Metal-Insulator Transition in Three Dimensions

Based on the spectral statistics obtained in numerical simulations on three dimensional disordered systems within the tight--binding approximation, a new superuniversal scaling relation is presented that allows us to collapse data for the orthogonal, unitary and symplectic symmetry ($\beta=1,2,4$) onto a single scaling curve. This relation provides a strong evidence for one-parameter scaling existing in these systems which exhibit a second order phase transition. As a result a possible one-parameter family of spacing distribution functions, $P_g(s)$, is given for each symmetry class $\beta$, where $g$ is the dimensionless conductance.Comment: 4 pages in PS including 3 figure

On random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.Comment: 4 pages, 5 figure

Spectra of complex networks

We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the case of networks with correlations between neighboring vertices. The tail of the density of eigenvalues $\rho(\lambda)$ at large $|\lambda|$ is related to the behavior of the vertex degree distribution $P(k)$ at large $k$. In particular, as $P(k) \sim k^{-\gamma}$, $\rho(\lambda) \sim |\lambda|^{1-2\gamma}$. We propose a simple approximation, which enables us to calculate spectra of various graphs analytically. We analyse spectra of various complex networks and discuss the role of vertices of low degree. We show that spectra of locally tree-like random graphs may serve as a starting point in the analysis of spectral properties of real-world networks, e.g., of the Internet.Comment: 10 pages, 4 figure

Chaos and the Quantum Phase Transition in the Dicke Model

We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of $N$ two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N \go \infty limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite $N$ and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.Comment: 51 pages, 15 figures, late

New Approaches in the Differentiation of Human Embryonic Stem Cells and Induced Pluripotent Stem Cells toward Hepatocytes

Orthotropic liver transplantation is the only established treatment for end-stage liver diseases. Utilization of hepatocyte transplantation and bio-artificial liver devices as alternative therapeutic approaches requires an unlimited source of hepatocytes. Stem cells, especially embryonic stem cells, possessing the ability to produce functional hepatocytes for clinical applications and drug development, may provide the answer to this problem. New discoveries in the mechanisms of liver development and the emergence of induced pluripotent stem cells in 2006 have provided novel insights into hepatocyte differentiation and the use of stem cells for therapeutic applications. This review is aimed towards providing scientists and physicians with the latest advancements in this rapidly progressing field

Clinical Use and Therapeutic Potential of IVIG/SCIG, Plasma-Derived IgA or IgM, and Other Alternative Immunoglobulin Preparations

Intravenous and subcutaneous immunoglobulin preparations, consisting of IgG class antibodies, are increasingly used to treat a broad range of pathological conditions, including humoral immune deficiencies, as well as acute and chronic inflammatory or autoimmune disorders. A plethora of Fab- or Fc-mediated immune regulatory mechanisms has been described that might act separately or in concert, depending on pathogenesis or stage of clinical condition. Attempts have been undertaken to improve the efficacy of polyclonal IgG preparations, including the identification of relevant subfractions, mild chemical modification of molecules, or modification of carbohydrate side chains. Furthermore, plasma-derived IgA or IgM preparations may exhibit characteristics that might be exploited therapeutically. The need for improved treatment strategies without increase in plasma demand is a goal and might be achieved by more optimal use of plasma-derived proteins, including the IgA and the IgM fractions. This article provides an overview on the current knowledge and future strategies to improve the efficacy of regular IgG preparations and discusses the potential of human plasma-derived IgA, IgM, and preparations composed of mixtures of IgG, IgA, and IgM

Random-Matrix Theory of Quantum Transport

This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal conductance fluctuations, weak localization, Coulomb blockade, sub-Poissonian shot noise, reflectionless tunneling into a superconductor, and giant conductance oscillations in a Josephson junction.Comment: 85 pages including 52 figures, to be published in Rev.Mod.Phy