Dual and anti-dual modes in dielectric spheres

We present how the angular momentum of light can play an important role to induce a dual or anti-dual behaviour on a dielectric particle. Although the material the particle is made of is not dual, i.e. a dielectric does not interact with an electrical field in the same way as it does with a magnetic one, a spherical particle can behave as a dual system when the correct excitation beam is chosen. We study the conditions under which this induced dual or anti-dual behaviour can be induced.Comment: 13 pages, 5 figure

From local to global analytic conjugacies

Let $f_1$ and $f_2$ be rational maps with Julia sets $J_1$ and $J_2$, and let $\Psi:J_1\to \mathbb{P}^1$ be any continuous map such that $\Psi\circ f_1=f_2\circ \Psi$ on $J_1$. We show that if $\Psi$ is $\mathbb{C}$-differentiable, with non-vanishing derivative, at some repelling periodic point $z_1\in J_1$, then $\Psi$ admits an analytic extension to $\mathbb{P}^1\setminus {\mathcal E}_1$, where ${\mathcal E}_1$ is the exceptional set of $f_1$. Moreover, this extension is a semiconjugacy. This generalizes a result of Julia (Ann. Sci. École Norm. Sup. (3) 40 (1923), 97–150). Furthermore, if ${\mathcal E}_1=\emptyset$ then the extended map $\Psi$ is rational, and in this situation $\Psi(J_1)=J_2$ and $\Psi^{-1}(J_2)=J_1$, provided that $\Psi$ is not constant. On the other hand, if ${\mathcal E}_1\neq \emptyset$ then the extended map may be transcendental: for example, when $f_1$ is a power map (conjugate to $z\mapsto z^{\pm d}$) or a Chebyshev map (conjugate to \pm \text{Х}_d with \text{Х}_d(z+z^{-1}) = z^d+z^{-d}), and when $f_2$ is an integral Lattès example (a quotient of the multiplication by an integer on a torus). Eremenko (Algebra i Analiz 1(4) (1989), 102–116) proved that these are the only such examples. We present a new proof

Absence of a true long-range orbital order in a two-leg Kondo ladder

We investigate, through the density-matrix renormalization group and the Lanczos technique, the possibility of a two-leg Kondo ladder present an incommensurate orbital order. Our results indicate a staggered short-range orbital order at half-filling. Away from half-filling our data are consistent with an incommensurate quasi-long-range orbital order. We also observed that an interaction between the localized spins enhances the rung-rung current correlations.Comment: 7 pages, 6 figures, changed the introduction and added some discussion

Power Euclidean metrics for covariance matrices with application to diffusion tensor imaging

Various metrics for comparing diffusion tensors have been recently proposed in the literature. We consider a broad family of metrics which is indexed by a single power parameter. A likelihood-based procedure is developed for choosing the most appropriate metric from the family for a given dataset at hand. The approach is analogous to using the Box-Cox transformation that is frequently investigated in regression analysis. The methodology is illustrated with a simulation study and an application to a real dataset of diffusion tensor images of canine hearts

Can the world feed itself? Some insights from growth theory

This paper develops a two-sector growth model incorporating the essential distinguishing features of agriculture, including the reliance of production on a natural resource base as well as on industrially produced inputs, the low income elasticity of demand for food and the life-sustaining function of food consumption. In this framework, the ability of an economy to supply an adequate supply of food to a growing population can be related to the existence of a steady state. This property is used to define a simple analytical criterion upon which to assess the long-term food situation of a closed economy. This sustainability condition relates all the dynamic parameters of the economy: rates of technological change in the two sectors, rate of population growth and rate of land degradation. The condition is used to highlight the technological characteristics in agriculture conducive to sustainability and to assess empirically the food situation of a number of countries. Although no global food crisis appears to be looming ahead, the data suggest that sub-Saharan Africa is likely to increase its food dependence in the future.Food Security and Poverty,

Outcome assessment after hip fracture : is EQ-5D the answer?

Objectives: To study the measurement properties of a joint specific patient reported outcome measure, a measure of capability and a general health-related quality of life (HRQOL) tool in a large cohort of patients with a hip fracture. Methods: Responsiveness and associations between the Oxford Hip Score (a hip specific measure: OHS), ICEpop CAPability (a measure of capability in older people: ICECAP-O) and EuroQol EQ-5D (general health-related quality of life measure: EQ-5D) were assessed using data available from two large prospective studies. The three outcome measures were assessed concurrently at a number of fixed follow-up time-points in a consecutive sequence of patients, allowing direct assessment of change from baseline, inter-measure associations and validity using a range of statistical methods. Results: ICECAP-O was not responsive to change. EQ-5D was responsive to change from baseline, with an estimated standardised effect size for the two datasets of 0.676 and 0.644 at six weeks and four weeks respectively; this was almost as responsive to change as OHS (1.14 at four weeks). EQ-5D correlated strongly with OHS; Pearson correlation coefficients were 0.74, 0.77 and 0.70 at baseline, four weeks and four months. EQ-5D is a moderately good predictor of death at 12 months following hip fracture. Furthermore, EQ-5D reported by proxies (relatives and carers) behaves similarly to self-reported scores. Conclusions: Our findings suggest that a general HRQOL tool such as EQ-5D could be used to measure outcome for patients recovering from hip fracture, including those with cognitive impairment

GROWTH PATTERN, SUSTAINABILITY AND TRADE IN A LAND CONSTRAINED ECONOMY

This paper develops a two-sector model of growth where agriculture is considered explicitly. Key features of the model include: the reliance of agricultural production on a fixed but degrading resource base, the use by the farm sector of industrially produced inputs and differing rates of technological progress in the two sectors. On the demand side, the low income elasticity for food as well as the life-sustaining function of food consumption are recognized. In this simplified framework, the sustainability of growth can be related to the existence of a steady state reflecting the ability of the economy to feed its population. This property is used to identify the characteristics within and outside of agriculture conducive to the sustainability of a land-constrained economy. The empirical application identifies sub-Saharan Africa as the region of the world facing the most important challenges in terms of sustainability. The second part of the paper makes use of the transitional properties of the model to analyse the relationship between agricultural productivity and growth performance. For a closed economy, the model unambiguously supports the view that high agricultural productivity is conducive to fast growth and industrialization. Once the country is allowed to trade, however, the relationship becomes more complex, but a numerical experiment illustrates how trade liberalization can accelerate the growth of a country poorly endowed in agricultural resources.sustainability, agriculture and growth, dynamic general equilibrium model, International Development, O41, O13, F11,