Frataxin deficiency increases cyclooxygenase 2 and prostaglandins in cell and animal models of Friedreich's ataxia.

An inherited deficiency of the mitochondrial protein frataxin causes Friedreich's ataxia (FRDA); the mechanism by which this deficiency triggers neuro- and cardio-degeneration is unclear. Microarrays of neural tissue of animal models of the disease showed decreases in antioxidant genes, and increases in inflammatory genes. Cyclooxygenase (COX)-derived oxylipins are important mediators of inflammation. We measured oxylipin levels using tandem mass spectrometry and ELISAs in multiple cell and animal models of FRDA. Mass spectrometry revealed increases in concentrations of prostaglandins, thromboxane B2, 15-HETE and 11-HETE in cerebellar samples of knockin knockout mice. One possible explanation for the elevated oxylipins is that frataxin deficiency results in increased COX activity. While constitutive COX1 was unchanged, inducible COX2 expression was elevated over 1.35-fold (P < 0.05) in two Friedreich's mouse models and Friedreich's lymphocytes. Consistent with higher COX2 expression, its activity was also increased by 58% over controls. COX2 expression is driven by multiple transcription factors, including activator protein 1 and cAMP response element-binding protein, both of which were elevated over 1.52-fold in cerebella. Taken together, the results support the hypothesis that reduced expression of frataxin leads to elevation of COX2-mediated oxylipin synthesis stimulated by increases in transcription factors that respond to increased reactive oxygen species. These findings support a neuroinflammatory mechanism in FRDA, which has both pathomechanistic and therapeutic implications

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.Comment: 17 pages, 9 Postscript figure

Multifractal properties of critical eigenstates in two-dimensional systems with symplectic symmetry

The multifractal properties of electronic eigenstates at the metal-insulator transition of a two-dimensional disordered tight-binding model with spin-orbit interaction are investigated numerically. The correlation dimensions of the spectral measure $\widetilde{D}_{2}$ and of the fractal eigenstate $D_{2}$ are calculated and shown to be related by $D_{2}=2\widetilde{D}_{2}$. The exponent $\eta=0.35\pm 0.05$ describing the energy correlations of the critical eigenstates is found to satisfy the relation $\eta=2-D_{2}$.Comment: 6 pages RevTeX; 3 uuencoded, gzipped ps-figures to appear in J. Phys. Condensed Matte

Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the framework of the generalized Chalker--Coddington network model. We determine the critical exponent $\alpha_0$ characterizing the scaling behavior of the local order parameter for systems with potential correlation length $d$ up to $12$ magnetic lengths $l$. Our results show that $\alpha_0$ does not depend on the ratio $d/l$. With increasing $d/l$, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behavior on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.Comment: 4 pages, 2 figures, postsript, uuencoded, gz-compresse

Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States

We present two novel approaches to establish the local density of states as an order parameter field for the Anderson transition problem. We first demonstrate for 2D quantum Hall systems the validity of conformal scaling relations which are characteristic of order parameter fields. Second we show the equivalence between the critical statistics of eigenvectors of the Hamiltonian and of the transfer matrix, respectively. Based on this equivalence we obtain the order parameter exponent $\alpha_0\approx 3.4$ for 3D quantum Hall systems.Comment: 4 pages, 3 Postscript figures, corrected scale in Fig.

Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis

We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.Comment: 10 pages, 13 figure

Multifractality of the quantum Hall wave functions in higher Landau levels

To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $\psi$ is studied for higher Landau levels, $N=1,2$, for various range $(\sigma )$ of random potential. We have found that, while the multifractal spectrum $f(\alpha)$ (and consequently the fractal dimension) does vary with $N$, the parabolic form for $f(\alpha)$ indicative of a log-normal distribution of $\psi$ persists in higher Landau levels. If we relate the multifractality with the scaling of localization via the conformal theory, an asymptotic recovery of the single-parameter scaling with increasing $\sigma$ is seen, in agreement with Huckestein's irrelevant scaling field argument.Comment: 10 pages, revtex, 5 figures available on request from [email protected]

Termination of Multifractal Behaviour for Critical Disordered Dirac Fermions

We consider Dirac fermions interacting with a disordered non-Abelian vector potential. The exact solution is obtained through a special type of conformal field theory including logarithmic correlators, without resorting to the replica or supersymmetry approaches. It is shown that the proper treatment of the conformal theory leads to a different multifractal scaling behaviour than initially expected. Moreover, the previous replica solution is found to be incorrect at the level of higher correlation functions.Comment: 4 pages, no figure

Exact Multifractality for Disordered N-Flavour Dirac Fermions in Two Dimensions

We present a nonperturbative calculation of all multifractal scaling exponents at strong disorder for critical wavefunctions of Dirac fermions interacting with a non-Abelian random vector potential in two dimensions. The results, valid for an arbitrary number of fermionic flavours, are obtained by deriving from Conformal Field Theory an effective Gaussian model for the wavefunction amplitudes and mapping to the thermodynamics of a single particle in a random potential. Our spectrum confirms that the wavefunctions remain delocalized in the presence of strong disorder.Comment: 4 pages, no figue

Metal-insulator transitions in anisotropic 2d systems

Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using transfer matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system (approximately 7/3). We also calculate the critical value of the scaling function for both the isotropic and the anisotropic system. It is found that the isotropic value equals the geometric mean of the two anisotropic values. Detailed numerical studies of the density of states for the isotropic system reveals that for an appreciable amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review