Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.Comment: 20 pages, 9 image

SU(1,1) symmetry of multimode squeezed states

We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation, and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations, and discuss its extension to more general quantum optical networks

Soil pathogen-aphid interactions under differences in soil organic matter and mineral fertilizer

There is increasing evidence showing that microbes can influence plant-insect interactions. In addition, various studies have shown that aboveground pathogens can alter the interactions between plants and insects. However, little is known about the role of soil-borne pathogens in plant-insect interactions. It is also not known how environmental conditions, that steer the performance of soil-borne pathogens, might influence these microbe-plant-insect interactions. Here, we studied effects of the soil-borne pathogen Rhizoctonia solani on aphids (Sitobion avenae) using wheat (Triticum aestivum) as a host. In a greenhouse experiment, we tested how different levels of soil organic matter (SOM) and fertilizer addition influence the interactions between plants and aphids. To examine the influence of the existing soil microbiome on the pathogen effects, we used both unsterilized field soil and sterilized field soil. In unsterilized soil with low SOM content, R. solani addition had a negative effect on aphid biomass, whereas it enhanced aphid biomass in soil with high SOM content. In sterilized soil, however, aphid biomass was enhanced by R. solani addition and by high SOM content. Plant biomass was enhanced by fertilizer addition, but only when SOM content was low, or in the absence of R. solani. We conclude that belowground pathogens influence aphid performance and that the effect of soil pathogens on aphids can be more positive in the absence of a soil microbiome. This implies that experiments studying the effect of pathogens under sterile conditions might not represent realistic interactions. Moreover, pathogen-plant-aphid interactions can be more positive for aphids under high SOM conditions. We recommend that soil conditions should be taken into account in the study of microbe-plant-insect interactions

Short-term western diet aggravates non-alcoholic fatty liver disease (NAFLD) with portal hypertension in TGR(mREN2)27 rats

Non-alcoholic fatty liver disease (NAFLD) is gaining in importance and is linked to obesity. Especially, the development of fibrosis and portal hypertension in NAFLD patients requires treatment. Transgenic TGR(mREN2)27 rats overexpressing mouse renin spontaneously develop NAFLD with portal hypertension but without obesity. This study investigated the additional role of obesity in this model on the development of portal hypertension and fibrosis. Obesity was induced in twelve-week old TGR(mREN2)27 rats after receiving Western diet (WD) for two or four weeks. Liver fibrosis was assessed using standard techniques. Hepatic expression of transforming growth factor-β1 (TGF-β1), collagen type Iα1, α-smooth muscle actin, and the macrophage markers Emr1, as well as the chemoattractant Ccl2, interleukin-1β (IL1β) and tumor necrosis factor-α (TNFα) were analyzed. Assessment of portal and systemic hemodynamics was performed using the colored microsphere technique. As expected, WD induced obesity and liver fibrosis as confirmed by Sirius Red and Oil Red O staining. The expression of the monocyte-macrophage markers, Emr1, Ccl2, IL1β and TNFα were increased during feeding of WD, indicating infiltration of macrophages into the liver, even though this increase was statistically not significant for the EGF module-containing mucin-like receptor (Emr1) mRNA expression levels. Of note, portal pressure increased with the duration of WD compared to animals that received a normal chow. Besides obesity, WD feeding increased systemic vascular resistance reflecting systemic endothelial and splanchnic vascular dysfunction. We conclude that transgenic TGR(mREN2)27 rats are a suitable model to investigate NAFLD development with liver fibrosis and portal hypertension. Tendency towards elevated expression of Emr1 is associated with macrophage activity point to a significant role of macrophages in NAFLD pathogenesis, probably due to a shift of the renin-angiotensin system towards a higher activation of the classical pathway. The hepatic injury induced by WD in TGR(mREN2)27 rats is suitable to evaluate different stages of fibrosis and portal hypertension in NAFLD with obesity

Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors

We show that any pair of real symmetric tensors \BGve and \BGm can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{\'e} and Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.Comment: 12 pages, no figure

Quantum Optical Systems for the Implementation of Quantum Information Processing

We review the field of Quantum Optical Information from elementary considerations through to quantum computation schemes. We illustrate our discussion with descriptions of experimental demonstrations of key communication and processing tasks from the last decade and also look forward to the key results likely in the next decade. We examine both discrete (single photon) type processing as well as those which employ continuous variable manipulations. The mathematical formalism is kept to the minimum needed to understand the key theoretical and experimental results

Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures

We present the theory of nonzero temperature ($T$) spin dynamics and transport in one-dimensional Heisenberg antiferromagnets with an energy gap $\Delta$. For $T << \Delta$, we develop a semiclassical picture of thermally excited particles. Multiple inelastic collisions between the particles are crucial, and are described by a two-particle S-matrix which has a super-universal form at low momenta. This is established by computations on the O(3) $\sigma$-model, and strong and weak coupling expansions (the latter using a Majorana fermion representation) for the two-leg S=1/2 Heisenberg antiferromagnetic ladder. As an aside, we note that the strong-coupling calculation reveals a S=1, two particle bound state which leads to the presence of a second peak in the T=0 inelastic neutron scattering (INS) cross-section for a range of values of momentum transfer. We obtain exact, or numerically exact, universal expressions for the thermal broadening of the quasi-particle peak in the INS cross-section, for the magnetization transport, and for the field dependence of the NMR relaxation rate $1/T_1$ of the effective semiclassical model: these are expected to be asymptotically exact for the quantum antiferromagnets. The results for $1/T_1$ are compared with the experimental findings of Takigawa et al and the agreement is quite good. In the regime $\Delta < T < (a typical microscopic exchange)$ we argue that a complementary description in terms of semiclassical waves applies, and give some exact results for the thermodynamics and dynamics.Comment: REVTEX, 53 pages and 23 postscript figures; added additional reference and associated clarificatio

Dynamics and transport near quantum-critical points

The physics of non-zero temperature dynamics and transport near quantum-critical points is discussed by a detailed study of the O(N)-symmetric, relativistic, quantum field theory of a N-component scalar field in $d$ spatial dimensions. A great deal of insight is gained from a simple, exact solution of the long-time dynamics for the N=1 d=1 case: this model describes the critical point of the Ising chain in a transverse field, and the dynamics in all the distinct, limiting, physical regions of its finite temperature phase diagram is obtained. The N=3, d=1 model describes insulating, gapped, spin chain compounds: the exact, low temperature value of the spin diffusivity is computed, and compared with NMR experiments. The N=3, d=2,3 models describe Heisenberg antiferromagnets with collinear N\'{e}el correlations, and experimental realizations of quantum-critical behavior in these systems are discussed. Finally, the N=2, d=2 model describes the superfluid-insulator transition in lattice boson systems: the frequency and temperature dependence of the the conductivity at the quantum-critical coupling is described and implications for experiments in two-dimensional thin films and inversion layers are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical properties of unconventional magnetic systems", Geilo, Norway, April 2-12, 1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be published. 46 page

Robust Signal Processing in Living Cells

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations