Random array of colour filters in the eyes of butterflies

The compound eye of the Japanese yellow swallowtail butterfly Papilio xuthus is not uniform, In a combined histological, electrophysiological and optical study, we found that the eye of P., xuthus has at least three different types of ommatidia, in a random distribution. In each ommatidium, nine photoreceptors contribute microvilli to the rhabdom, The distal two-thirds of the rhabdom length is taken up by the rhabdomeres of photoreceptors R1-R4, The proximal third consists of rhabdomeres of photoreceptors R5-R8, except for the very basal part, to which photoreceptor R9 contributes, In all ommatidia, the R1 and R2 photoreceptors have a purple pigmentation positioned at the distal tip of the ommatidia, The R3-R8 photoreceptors in any one ommatidium all have either yellow or red pigmentation in the cell body, concentrated near the edge of the rhabdom, The ommatidia with red-pigmented R3-R8 are divided into two classes: one class contains an ultraviolet-fluorescing pigment. The different pigmentations are presumably intimately related to the various spectral types found previously in electrophysiological studies.</p

Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field

The dynamical spin structure factor S^{zz}(Q,omega) in the small momentum region is derived analytically for the one-dimensional supersymmetric t-J model with 1/r^2 interaction. Strong spin-charge separation is found in the spin dynamics. The structure factor S^{zz}(Q,omega) with a given spin polarization does not depend on the electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S^{zz}(Q,omega). These results are derived via solution of the SU(2,1) Sutherland model in the strong coupling limit.Comment: 20 pages, 8 figures. Accepted for publication in J.Phys.

Retinal regionalization and heterogeneity of butterfly eyes

The regional characteristics of the eyes of butterflies from different families have been surveyed using epi-illumination microscopy, utilizing the eyeshine visible due to the tapetum situated proximally to the rhabdom. All butterflies studied have a high spatial acuity in the frontal region. The facet diameter varies slightly across the eye, and the interommatidial angle and the eye parameter p are especially large dorsally. Whereas the ommatidial lattice is generally highly regular, the eyeshine colours distinctly depend on the species. Sometimes the eyeshine is locally uniform, but often it is heterogeneous. It is hypothesized that the regional characteristics as well as the local heterogeneity are adaptations that optimize spectral discrimination

Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method

Hole propagator of spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator on Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator on gl_2-Jack polynomials by the mapping. The resultant expression for hole propagator for finite-size system is written in terms of renormalized momenta and spin of quasi-holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of spin Calogero-Sutherland model becomes equivalent to dynamical colour correlation function of SU(3) Haldane-Shastry model.Comment: 36 pages, 8 figure

Ommatidial heterogeneity in the compound eye of the male small white butterfly, Pieris rapae crucivora

The ommatidia in the ventral two-thirds of the compound eye of male Pieris rapae crucivora are not uniform. Each ommatidium contains nine photoreceptor cells. Four cells (R1-4) form the distal two-thirds of the rhabdom, four cells (R5-8) approximately occupy the proximal one-third of the rhabdom, and the ninth cell (R9) takes up a minor basal part of the rhabdom. The R5-8 photoreceptor cells contain clusters of reddish pigment adjacent to the rhabdom. From the position of the pigment clusters, three types of ommatidia can be identified: the trapezoidal (type I), square (type II), and rectangular type (type III). Microspectrophotometry with an epi-illumination microscope has revealed that the reflectance spectra of type I and type III ommatidia peak at 635 nm and those of type II ommatidia peak at 675 nm. The bandwith of the reflectance spectra is 40-50 nm. Type II ommatidia strongly fluoresce under ultra-violet and violet epi-illumination. The three types of ommatidia are randomly distributed. The ommatidial heterogeneity is presumably crucial for color discrimination