Mixture models of nucleotide sequence evolution that account for heterogeneity in the substitution process across sites and across lineages.

Molecular phylogenetic studies of homologous sequences of nucleotides often assume that the underlying evolutionary process was globally stationary, reversible, and homogeneous (SRH), and that a model of evolution with one or more site-specific and time-reversible rate matrices (e.g., the GTR rate matrix) is enough to accurately model the evolution of data over the whole tree. However, an increasing body of data suggests that evolution under these conditions is an exception, rather than the norm. To address this issue, several non-SRH models of molecular evolution have been proposed, but they either ignore heterogeneity in the substitution process across sites (HAS) or assume it can be modeled accurately using the distribution. As an alternative to these models of evolution, we introduce a family of mixture models that approximate HAS without the assumption of an underlying predefined statistical distribution. This family of mixture models is combined with non-SRH models of evolution that account for heterogeneity in the substitution process across lineages (HAL). We also present two algorithms for searching model space and identifying an optimal model of evolution that is less likely to over- or underparameterize the data. The performance of the two new algorithms was evaluated using alignments of nucleotides with 10 000 sites simulated under complex non-SRH conditions on a 25-tipped tree. The algorithms were found to be very successful, identifying the correct HAL model with a 75% success rate (the average success rate for assigning rate matrices to the tree's 48 edges was 99.25%) and, for the correct HAL model, identifying the correct HAS model with a 98% success rate. Finally, parameter estimates obtained under the correct HAL-HAS model were found to be accurate and precise. The merits of our new algorithms were illustrated with an analysis of 42 337 second codon sites extracted from a concatenation of 106 alignments of orthologous genes encoded by the nuclear genomes of Saccharomyces cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, S. castellii, S. kluyveri, S. bayanus, and Candida albicans. Our results show that second codon sites in the ancestral genome of these species contained 49.1% invariable sites, 39.6% variable sites belonging to one rate category (V1), and 11.3% variable sites belonging to a second rate category (V2). The ancestral nucleotide content was found to differ markedly across these three sets of sites, and the evolutionary processes operating at the variable sites were found to be non-SRH and best modeled by a combination of eight edge-specific rate matrices (four for V1 and four for V2). The number of substitutions per site at the variable sites also differed markedly, with sites belonging to V1 evolving slower than those belonging to V2 along the lineages separating the seven species of Saccharomyces. Finally, sites belonging to V1 appeared to have ceased evolving along the lineages separating S. cerevisiae, S. paradoxus, S. mikatae, S. kudriavzevii, and S. bayanus, implying that they might have become so selectively constrained that they could be considered invariable sites in these species.

Imaging performance of finite uniaxial metamaterials with large anisotropy.

Metamaterials with extreme anisotropy overcome the diffraction limit by supporting the propagation of otherwise evanescent waves. Recent experiments in slabs of wire media have shown that images deteriorate away from the longitudinal Fabry-Perot resonances of the slab. Existing theoretical models explain this using nonlocality, surface waves, and additional boundary conditions. We show that image aberrations can be understood as originating from cavity resonances of uniaxial media with large local axial permittivity. We apply a simple cavity resonator model and a transfer matrix approach to replicate salient experimental features of wire media hyperlenses. These results offer avenues to reduce observed imaging artefacts, and are applicable to all uniaxial media with large magnitude of the axial permittivity, e.g., wire media and layered media.

Two stationary nonhomogeneous Markov models of nucleotide sequence evolution.

The general Markov model (GMM) of nucleotide substitution does not assume the evolutionary process to be stationary, reversible, or homogeneous. The GMM can be simplified by assuming the evolutionary process to be stationary. A stationary GMM is appropriate for analyses of phylogenetic data sets that are compositionally homogeneous; a data set is considered to be compositionally homogeneous if a statistical test does not detect significant differences in the marginal distributions of the sequences. Though the general time-reversible (GTR) model assumes stationarity, it also assumes reversibility and homogeneity. We propose two new stationary and nonhomogeneous models--one constrains the GMM to be reversible, whereas the other does not. The two models, coupled with the GTR model, comprise a set of nested models that can be used to test the assumptions of reversibility and homogeneity for stationary processes. The two models are extended to incorporate invariable sites and used to analyze a seven-taxon hominoid data set that displays compositional homogeneity. We show that within the class of stationary models, a nonhomogeneous model fits the hominoid data better than the GTR model. We note that if one considers a wider set of models that are not constrained to be stationary, then an even better fit can be obtained for the hominoid data. However, the methods for reducing model complexity from an extremely large set of nonstationary models are yet to be developed.

Circular and elliptical birefringence in spun microstructured optical fibres.

We investigate circular birefringence induced by spinning microstructured optical fibres during their fabrication to produce helical-shaped holes. Designs with an offset core which results in a helical path for the light and exhibit only circular birefringence and designs with a linearly birefringent core that result in elliptical birefringence are both investigated.

Iridescence from photonic crystals and its suppression in butterfly scales.

Regular three-dimensional periodic structures have been observed in the scales of over half a dozen butterfly species. We compare several of these structures: we calculate their photonic bandgap properties; measure the angular variation of the reflection spectra; and relate the observed iridescence (or its suppression) to the structures. We compare the mechanisms for iridescence suppression in different species and conclude with some speculations about form, function, development and evolution.

Color, iridescence, and thermoregulation in Lepidoptera.

This paper examines evidence for the hypothesized connection between solar thermal properties of butterfly and moth (Lepidoptera) wings, iridescence/structural color, and thermoregulation. Specimens of 64 species of Lepidoptera were measured spectrophotometrically, their solar absorptances calculated, and their habitat temperatures determined. No correlation was found between habitat temperature and the solar absorptance of the wings. It was found, however, that the iridescent specimens exhibited, on average, substantially higher solar absorptance than noniridescent ones.

Exaggeration and suppression of iridescence: the evolution of two-dimensional butterfly structural colours.

Many butterfly species possess 'structural' colour, where colour is due to optical microstructures found in the wing scales. A number of such structures have been identified in butterfly scales, including three variations on a simple multi-layer structure. In this study, we optically characterize examples of all three types of multi-layer structure, as found in 10 species. The optical mechanism of the suppression and exaggeration of the angle-dependent optical properties (iridescence) of these structures is described. In addition, we consider the phylogeny of the butterflies, and are thus able to relate the optical properties of the structures to their evolutionary development. By applying two different types of analysis, the mechanism of adaptation is addressed. A simple parsimony analysis, in which all evolutionary changes are given an equal weighting, suggests convergent evolution of one structure. A Dollo parsimony analysis, in which the evolutionary 'cost' of losing a structure is less than that of gaining it, implies that 'latent' structures can be reused.

Multi-objective and constrained design of fibre Bragg gratings using Evolutionary Algorithms.

We apply a multi-objective evolutionary algorithm to a grating problem where only very specific features of the transmission spectrum are specified during the optimisation process. The design problem analysed here relates to the passive extraction of 10 GHz clock signals from a 10 Gbps OTDM RZ encoded data stream. Four spectral features of interest such as bandwidth and passband quality are explicitly defined. Using a real-encoded evolutionary algorithm along with an elitist multi-objective selection method, we arrive at a group of solutions which each satisfy the objectives to various degrees in the presence of manufacturing and other design constraints.

Small-core single-mode microstructured polymer optical fiber with large external diameter.

A preform sleeving technique is demonstrated that allows the fabrication of single-mode polymer microstructured fiber with the smallest core and hole dimensions yet reported to our knowledge. For a fixed triangular hole pattern a range of fibers is produced by adjustment to the operating conditions of the draw tower. Numerical modeling is carried out for one of the fibers produced with a 570-microm external diameter, a core diameter of 2.23 microm, an average hole diameter of 0.53 microm, and an average hole spacing of 1.38 microm. This fiber was shown to be endlessly single mode.

Antisymmetric grating coupler: experimental results.

The principle of an antisymmetric grating coupler was recently proposed theoretically as a planar waveguide add-drop multiplexer. It has the potential to enhance significantly the functionality of an add-drop multiplexer based on grating-assisted coupling. Here we realize the concept experimentally in an all-fiber geometry. We show that conventional devices exhibit two high-reflection bands. In contrast, the antisymmetric grating coupler has only a single reflection band, thereby dramatically improving its filtering characteristics.

Novel characterization technique with 0.5 ppm spatial accuracy of fringe period in Bragg gratings.

We demonstrate a novel method that can detect period fluctuations of periodic structures such as fiber Bragg gratings at an accuracy of approximately 0.5 ppm. These fluctuations can consist of chirp rates, phase shifts etc. The method can also be used to measure phase masks or work as a position control device with spatial resolution in the order of 10 nm. The technique is a modified side diffraction method with interference between two diffraction orders.

Fourier decomposition algorithm for leaky modes of fibres with arbitrary geometry.

A new algorithm for calculating the confinement loss of leaky modes in arbitrary fibre structures is presented within the scalar wave approximation. The algorithm uses a polar-coordinate Fourier decomposition method with adjustable boundary conditions (ABC-FDM) to model the outward radiating .elds. Leaky modes are calculated for different examples of microstructured fibres with various shaped holes.