Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.

Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to 100 x 100 x 100 lattice sites. The scaling behavior of the level statistics is examined for large spacings near the delocalization-localization transition and the correlation length exponent is found. By using high-precision calculations we conjecture a new interpolation of the critical cumulative probability, which has size-independent asymptotic form \ln I(s) \propto -s^{\alpha} with \alpha = 1.0 \pm 0.1.Comment: 5 pages, RevTex, 4 figures, to appear in Physical Review Letter

Anderson transition in three-dimensional disordered systems with symplectic symmetry

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.Comment: 4 pages, revtex, to appear in Physical Review Letters. 3 figures available on request either by fax or normal mail from [email protected] or [email protected]

Random Matrix Theory of the Energy-Level Statistics of Disordered Systems at the Anderson Transition

We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, $V(\epsilon)\sim {A\over 2}\ln ^2(\epsilon)$. The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when $A<1$. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME with weak confinement. For $A_c\approx 0.4$ the distribution function of the energy-level spacings (LSDF) of this RME coincides in a large energy window with the LSDF of the three dimensional Anderson model at the metal-insulator transition. For the same $A_c$, the variance of the number of levels, $\langle n^2\rangle -\langle n\rangle^2$, in an interval containing $\langle n\rangle$ levels on average, grows linearly with $\langle n\rangle$, and its slope is equal to $0.32 \pm 0.02$, which is consistent with the value found for the Anderson model at the critical point.Comment: 32 pages, REVTEX 3.0, 10 postscript (uuencoded) figures include

Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition

The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is ``compressible'', in the sense that the variance of the level number in an interval is $= \chi$ for $>> 1$. The compressibility, $\chi=\eta/2d$, is given ``exactly'' in terms of the multifractal exponent $\eta=d-D_2$ at the mobility edge in a $d$-dimensional system.Comment: 10 pages in REVTeX preprint format; to be published in JETP Letters, 199

Three-Dimensional Quantum Percolation Studied by Level Statistics

Three-dimensional quantum percolation problems are studied by analyzing energy level statistics of electrons on maximally connected percolating clusters. The quantum percolation threshold \pq, which is larger than the classical percolation threshold \pc, becomes smaller when magnetic fields are applied, i.e., \pq(B=0)>\pq(B\ne 0)>\pc. The critical exponents are found to be consistent with the recently obtained values of the Anderson model, supporting the conjecture that the quantum percolation is classified onto the same universality classes of the Anderson transition. Novel critical level statistics at the percolation threshold is also reported.Comment: to appear in the May issue of J. Phys. Soc. Jp

Magnetolocalization in disordered quantum wires

The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results on magnetolocalization is included.Comment: 22 pages, RevTe

High-risk human papillomavirus infections in breast cancer in Syrian women and their association with Id-1 expression: a tissue microarray study

High-risk human papillomaviruses (HPVs) could be important risk factors for breast carcinogenesis and metastasis. Based on this hypothesis, we recently studied the effect of E6/E7 onco-proteins of high-risk HPV type 16 in two non-invasive human breast cancer cell lines, BT20 and MCF7; we reported that E6/E7 converts these cell lines to invasive cells. This is accompanied by an overexpression of Id-1, which is an important regulator of breast metastasis. In this investigation, we examined the presence of high-risk HPVs (16, 18, 31, 33 and 35) and the expression of their E6 onco-protein as well as their correlation with Id-1 gene expression, using polymerase chain reaction (PCR) and tissue microarray (TMA) analysis, respectively, in a cohort of 113 Syrian breast cancer patients. We found that high-risk HPV types 16, 18, 31, 33 and 35 are present in 8.84, 9.73, 7.07, 55.75 and 37.16% of our samples, respectively, which represent invasive breast cancers. Overall, 69 (61.06%) of the 113 samples are HPV positive; among these specimens 24 tissues (34.78%) are coinfected with more than one HPV type. Furthermore, we report that the expression of the E6 onco-protein of these high-risk HPVs is correlated with Id-1 overexpression in the majority of invasive breast cancer tissue samples. Our data suggest that high-risk HPV infections are associated with human breast cancer progression in Syrian women

Functional Interactions between the erupted/tsg101 Growth Suppressor Gene and the DaPKC and rbf1 Genes in Drosophila Imaginal Disc Tumors

BACKGROUND: The Drosophila gene erupted (ept) encodes the fly homolog of human Tumor Susceptibility Gene-101 (TSG101), which functions as part of the conserved ESCRT-1 complex to facilitate the movement of cargoes through the endolysosomal pathway. Loss of ept or other genes that encode components of the endocytic machinery (e.g. synatxin7/avalanche, rab5, and vps25) produces disorganized overgrowth of imaginal disc tissue. Excess cell division is postulated to be a primary cause of these 'neoplastic' phenotypes, but the autonomous effect of these mutations on cell cycle control has not been examined. PRINCIPAL FINDINGS: Here we show that disc cells lacking ept function display an altered cell cycle profile indicative of deregulated progression through the G1-to-S phase transition and express reduced levels of the tumor suppressor ortholog and G1/S inhibitor Rbf1. Genetic reductions of the Drosophila aPKC kinase (DaPKC), which has been shown to promote tumor growth in other fly tumor models, prevent both the ept neoplastic phenotype and the reduction in Rbf1 levels that otherwise occurs in clones of ept mutant cells; this effect is coincident with changes in localization of Notch and Crumbs, two proteins whose sorting is altered in ept mutant cells. The effect on Rbf1 can also be blocked by removal of the gamma-secretase component presenilin, suggesting that cleavage of a gamma-secretase target influences Rbf1 levels in ept mutant cells. Expression of exogenous rbf1 completely ablates ept mutant eye tissues but only mildly affects the development of discs composed of cells with wild type ept. CONCLUSIONS: Together, these data show that loss of ept alters nuclear cell cycle control in developing imaginal discs and identify the DaPKC, presenilin, and rbf1 genes as modifiers of molecular and cellular phenotypes that result from loss of ept

Small group interventions for children aged 5-9 years old with mathematical learning difficulties

The research related to educational interventions for children with mathematical learning difficulties has been increasing steadily. In this chapter I focus on small group interventions for children aged 5–9 years old with learning difficulties in mathematics. First, I describe the important issues: (1) who are the children having problems in mathematics, (2) what do we mean with (special) education intervention, (3) what does Responsiveness to Intervention mean, and (4) what intervention features have been found effective for children aged 5–9 years with learning difficulties in mathematics. Then, I describe the research and developmental work that has been done in Finland on designing web services which provide evidence-based information and materials for educators. The two web services are LukiMat and ThinkMath. Together, these two web services include the knowledge base, assessment batteries and intervention tools to be used in relation to mathematical learning difficulties in the age group 5–9 years.Peer reviewe