Limb reduction in squamate reptiles correlates with the reduction of the chondrocranium: A case study on serpentiform anguids

Abstract Background In vertebrates, the skull evolves from a complex network of dermal bones and cartilage?the latter forming the pharyngeal apparatus and the chondrocranium. Squamates are particularly important in this regard as they maintain at least part of the chondrocranium throughout their whole ontogeny until adulthood. Anguid lizards represent a unique group of squamates, which contains limbed and limbless forms and show conspicuous variation of the adult skull. Results Based on several emboadryonic stages of the limbless lizards Pseudopus apodus and Anguis fragilis, and by comparing with other squamates, we identified and interpreted major differences in chondrocranial anatomy. Among others, the most important differences are in the orbitotemporal region. P. apodus shows a strikingly similar development of this region to other squamates. Unexpectedly, however, A. fragilis differs considerably in the composition of the orbitotemporal region. In addition, A. fragilis retains a paedomorphic state of the nasal region. Conclusions Taxonomic comparisons indicate that even closely related species with reduced limbs show significant differences in chondrocranial anatomy. The Pearson correlation coefficient suggests strong correlation between chondrocranial reduction and limb reduction. We pose the hypothesis that limb reduction could be associated with the reduction in chondrocrania by means of genetic mechanisms

Interfering resonances in a quantum billiard

We present a method for numerically obtaining the positions, widths and wavefunctions of resonance states in a two dimensional billiard connected to a waveguide. For a rectangular billiard, we study the dynamics of three resonance poles lying separated from the other ones. As a function of increasing coupling strength between the waveguide and the billiard two of the states become trapped while the width of the third one continues to increase for all coupling strengths. This behavior of the resonance poles is reflected in the time delay function which can be studied experimentally.Comment: 2 pages, 3 figure

S-matrix theory for transmission through billiards in tight-binding approach

In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles.Comment: 29 pages, 9 figures, submitted to J. Phys. A: Math. and Ge

Hall-like effect induced by spin-orbit interaction

The effect of spin-orbit interaction on electron transport properties of a cross-junction structure is studied. It is shown that it results in spin polarization of left and right outgoing electron waves. Consequently, incoming electron wave of a proper polarization induces voltage drop perpendicularly to the direct current flow between source and drain of the considered four-terminal cross-structure. The resulting Hall-like resistance is estimated to be of the order of 10^-3 - 10^-2 h/e^2 for technologically available structures. The effect becomes more pronounced in the vicinity of resonances where Hall-like resistance changes its sign as function of the Fermi energy.Comment: 4 pages (RevTeX), 4 figures, will appear in Phys. Rev. Let

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Observation of Quantum Asymmetry in an Aharonov-Bohm Ring

We have investigated the Aharonov-Bohm effect in a one-dimensional GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of these systems are for the first time systematically studied as a function of density. We observe phase-shifts of $\pi$ in the magnetoconductance oscillations, and halving of the fundamental $h/e$ period, as the density is varied. Theoretically we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.

Conductance of Open Quantum Billiards and Classical Trajectories

We analyse the transport phenomena of 2D quantum billiards with convex boundary of different shape. The quantum mechanical analysis is performed by means of the poles of the S-matrix while the classical analysis is based on the motion of a free particle inside the cavity along trajectories with a different number of bounces at the boundary. The value of the conductance depends on the manner the leads are attached to the cavity. The Fourier transform of the transmission amplitudes is compared with the length of the classical paths. There is good agreement between classical and quantum mechanical results when the conductance is achieved mainly by special short-lived states such as whispering gallery modes (WGM) and bouncing ball modes (BBM). In these cases, also the localization of the wave functions agrees with the picture of the classical paths. The S-matrix is calculated classically and compared with the transmission coefficients of the quantum mechanical calculations for five modes in each lead. The number of modes coupled to the special states is effectively reduced.Comment: 19 pages, 6 figures (jpg), 2 table

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.Comment: 5 pages, 5 figure

The evolutionary dynamics of extrachromosomal DNA in human cancers

Oncogene amplification on extrachromosomal DNA (ecDNA) is a common event, driving aggressive tumor growth, drug resistance and shorter survival. Currently, the impact of nonchromosomal oncogene inheritance-random identity by descent-is poorly understood. Also unclear is the impact of ecDNA on somatic variation and selection. Here integrating theoretical models of random segregation, unbiased image analysis, CRISPR-based ecDNA tagging with live-cell imaging and CRISPR-C, we demonstrate that random ecDNA inheritance results in extensive intratumoral ecDNA copy number heterogeneity and rapid adaptation to metabolic stress and targeted treatment. Observed ecDNAs benefit host cell survival or growth and can change within a single cell cycle. ecDNA inheritance can predict, a priori, some of the aggressive features of ecDNA-containing cancers. These properties are facilitated by the ability of ecDNA to rapidly adapt genomes in a way that is not possible through chromosomal oncogene amplification. These results show how the nonchromosomal random inheritance pattern of ecDNA contributes to poor outcomes for patients with cancer

Simulations of interference effects in gated two-dimensional ballistic electron systems

We present detailed simulations addressing recent electronic interference experiments, where a metallic gate is used to locally modify the Fermi wave-length of the charge carriers. Our numerical calculations are based on a solution of the one-particle Schroedinger equation for a realistic model of the actual sample geometry, including a Poisson equation based determination of the potential due to the gate. The conductance is determined with the multiprobe Landauer-Buettiker formula, and in general we find conductance vs. gate voltage characteristics which closely resemble the experimental traces. A detailed examination based on quantum mechanical streamlines suggests that the simple one-dimensional semiclassical model often used to describe the experiments has only a limited range of validity, and that certain 'unexpected' periodicities should not be assigned any particular significance, they arise due to the complicated multiple scattering processes occurring in certain sample geometries.Comment: 7 pages, 10 embedded figures, higher quality figures available in tif-format (or as a hard copy) from [email protected]