Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. This is in good agreement with recent analytical results.Comment: 14 pages in plain TeX, 6 figures upon reques

On beta-Plurality Points in Spatial Voting Games

Let $V$ be a set of $n$ points in $\mathbb{R}^d$, called voters. A point $p\in \mathbb{R}^d$ is a plurality point for $V$ when the following holds: for every $q\in\mathbb{R}^d$ the number of voters closer to $p$ than to $q$ is at least the number of voters closer to $q$ than to $p$. Thus, in a vote where each $v\in V$ votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal $p$ will not lose against any alternative proposal $q$. For most voter sets a plurality point does not exist. We therefore introduce the concept of $\beta$-plurality points, which are defined similarly to regular plurality points except that the distance of each voter to $p$ (but not to $q$) is scaled by a factor $\beta$, for some constant $0<\beta\leq 1$. We investigate the existence and computation of $\beta$-plurality points, and obtain the following. * Define \beta^*_d := \sup \{ \beta : \text{any finite multiset V$in$\mathbb{R}^d$admits a$\beta-plurality point} \}. We prove that $\beta^*_2 = \sqrt{3}/2$, and that $1/\sqrt{d} \leq \beta^*_d \leq \sqrt{3}/2$ for all $d\geq 3$. * Define \beta(p, V) := \sup \{ \beta : \text{p$is a$\beta$-plurality point for$V}\}. Given a voter set $V \in \mathbb{R}^2$, we provide an algorithm that runs in $O(n \log n)$ time and computes a point $p$ such that $\beta(p, V) \geq \beta^*_2$. Moreover, for $d\geq 2$ we can compute a point $p$ with $\beta(p,V) \geq 1/\sqrt{d}$ in $O(n)$ time. * Define \beta(V) := \sup \{ \beta : \text{V$admits a$\beta-plurality point}\}. We present an algorithm that, given a voter set $V$ in $\mathbb{R}^d$, computes an $(1-\varepsilon)\cdot \beta(V)$ plurality point in time $O(\frac{n^2}{\varepsilon^{3d-2}} \cdot \log \frac{n}{\varepsilon^{d-1}} \cdot \log^2 \frac {1}{\varepsilon})$.Comment: 21 pages, 10 figures, SoCG'2

Energy Dose-Response in Selective Laser Trabeculoplasty: A Review

PRCIS: A literature review of SLT energy dose response found no definitive relationship between IOP reduction with respect to total or pulse energy, race, pigmentation, or application pattern. PURPOSE: Selective laser trabeculoplasty (SLT) is a safe and effective treatment for lowering intraocular pressure (IOP). While evidence is mounting for the advantage of its use as a first-line treatment for IOP reduction, the SLT procedures in use vary widely. The purpose of this literature review was to investigate if there were any relationships between SLT energy and efficacy for lowering IOP in the published literature. METHODS: A literature review was undertaken that included studies in which energy levels required for successful SLT treatment were investigated: in general, with respect to angle pigmentation, race or ethnicity, and treatment arc extent. RESULTS: There was no indication that higher (or lower) energy used in the treatment leads to greater (or less) IOP reduction. Similar results were obtained regarding level of trabecular meshwork (TM) pigmentation. Race was not found to be associated with altered dose response in SLT. There were indications that treating the full 360 degrees, as opposed to smaller arcs, could be beneficial for more IOP reduction. IOP reduction from SLT was found to be similar to that provided by topical medications. CONCLUSIONS: The optimal energy level of SLT needed for IOP reduction has not yet been definitively established, with all reported pulse energies resulting in similar IOP reduction. Furthermore, similar lack of conclusive findings exists regarding optimal SLT energy dosage for use in different races and degrees of TM pigmentation. This parameter, as well as each of the above-mentioned factors, requires further research

Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices

We study statistical properties of the ensemble of large $N\times N$ random matrices whose entries $H_{ij}$ decrease in a power-law fashion $H_{ij}\sim|i-j|^{-\alpha}$. Mapping the problem onto a nonlinear $\sigma-$model with non-local interaction, we find a transition from localized to extended states at $\alpha=1$. At this critical value of $\alpha$ the system exhibits multifractality and spectral statistics intermediate between the Wigner-Dyson and Poisson one. These features are reminiscent of those typical for the mobility edge of disordered conductors. We find a continuous set of critical theories at $\alpha=1$, parametrized by the value of the coupling constant of the $\sigma-$model. At $\alpha>1$ all states are expected to be localized with integrable power-law tails. At the same time, for $1<\alpha<3/2$ the wave packet spreading at short time scale is superdiffusive: $\langle |r|\rangle\sim t^{\frac{1}{2\alpha-1}}$, which leads to a modification of the Altshuler-Shklovskii behavior of the spectral correlation function. At $1/2<\alpha<1$ the statistical properties of eigenstates are similar to those in a metallic sample in $d=(\alpha-1/2)^{-1}$ dimensions. Finally, the region $\alpha<1/2$ is equivalent to the corresponding Gaussian ensemble of random matrices $(\alpha=0)$. The theoretical predictions are compared with results of numerical simulations.Comment: 19 pages REVTEX, 4 figure

Ferromagnetic/superconducting proximity effect in La0.7Ca0.3MnO3 / YBa2Cu3O7 superlattices

We study the interplay between magnetism and superconductivity in high quality YBa2Cu3O7 (YBCO) / La0.7Ca0.3MnO3(LCMO)superlattices. We find evidence for the YBCO superconductivity depression in presence of the LCMO layers. We show that due to its short coherence length superconductivity survives in the YBCO down to much smaller thickness in presence of the magnetic layer than in low Tc superconductors. We also find that for a fixed thickness of the superconducting layer, superconductivity is depressed over a thickness interval of the magnetic layer in the 100 nm range. This is a much longer length scale than that predicted by the theory of ferromagnetic/superconducting proximity effect.Comment: 10 pages + 5 figures, submitted to Phys. Rev.

Aharonov-Bohm effect in the chiral Luttinger liquid

Edge states of the quantum Hall fluid provide an almost unparalled opportunity to study mesoscopic effects in a highly correlated electron system. In this paper we develop a bosonization formalism for the finite-size edge state, as described by chiral Luttinger liquid theory, and use it to study the Aharonov-Bohm effect. The problem we address may be realized experimentally by measuring the tunneling current between two edge states through a third edge state formed around an antidot in the fractional quantum Hall effect regime. A renormalization group analysis reveals the existence of a two-parameter universal scaling function G(X,Y) that describes the Aharonov-Bohm resonances. We also show that the strong renormalization of the tunneling amplitudes that couple the antidot to the incident edge states, together with the nature of the Aharonov-Bohm interference process in a chiral system, prevent the occurrence of perfect resonances as the magnetic field is varied, even at zero temperature.Comment: 16 pages, Revtex, 5 figures available from [email protected]

Motion Planning via Manifold Samples

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming. This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice. We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.Comment: 18 page

Dynamic Modelling under Uncertainty: The Case of Trypanosoma brucei Energy Metabolism

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies

The expression and activity of β-catenin in the thalamus and its projections to the cerebral cortex in the mouse embryo

<p>Abstract</p> <p>Background</p> <p>The mammalian thalamus relays sensory information from the periphery to the cerebral cortex for cognitive processing via the thalamocortical tract. The thalamocortical tract forms during embryonic development controlled by mechanisms that are not fully understood. β-catenin is a nuclear and cytosolic protein that transduces signals from secreted signaling molecules to regulate both cell motility via the cytoskeleton and gene expression in the nucleus. In this study we tested whether β-catenin is likely to play a role in thalamocortical connectivity by examining its expression and activity in developing thalamic neurons and their axons.</p> <p>Results</p> <p>At embryonic day (E)15.5, the time when thalamocortical axonal projections are forming, we found that the thalamus is a site of particularly high β-catenin mRNA and protein expression. As well as being expressed at high levels in thalamic cell bodies, β-catenin protein is enriched in the axons and growth cones of thalamic axons and its growth cone concentration is sensitive to Netrin-1. Using mice carrying the β-catenin reporter <it>BAT-gal </it>we find high levels of reporter activity in the thalamus. Further, Netrin-1 induces <it>BAT-gal </it>reporter expression and upregulates levels of endogenous transcripts encoding β-actin and L1 proteins in cultured thalamic cells. We found that β-catenin mRNA is enriched in thalamic axons and its 3'UTR is phylogenetically conserved and is able to direct heterologous mRNAs along the thalamic axon, where they can be translated.</p> <p>Conclusion</p> <p>We provide evidence that β-catenin protein is likely to be an important player in thalamocortcial development. It is abundant both in the nucleus and in the growth cones of post-mitotic thalamic cells during the development of thalamocortical connectivity and β-catenin mRNA is targeted to thalamic axons and growth cones where it could potentially be translated. β-catenin is involved in transducing the Netrin-1 signal to thalamic cells suggesting a mechanism by which Netrin-1 guides thalamocortical development.</p