Topological Charge and Asymptotic Phase Invariants of Vortex Laser Beams

It is well known that the orbital angular momentum (OAM) of a light field is conserved on propagation. In this work, in contrast to the OAM, we analytically study conservation of the topological charge (TC), which is often confused with OAM, but has quite different physical meaning. To this end, we propose a huge-ring approximation of the Huygens–Fresnel principle, when the observation point is located on an infinite-radius ring. Based on this approximation, our proof of TC conservation reveals that there exist other quantities that are also propagation-invariant, and the number of these invariants is theoretically infinite. Numerical simulation confirms the conservation of two such invariants for two light fields. The results of this work can find applications in optical data transmission to identify optical signals.

Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.

Individual growth profiling improves growth modelling in the geoduck clam Panopea generosa

Contemporary modelling of growth based on shell-length to terminal age (SLTA) in long-lived clams is subject to inaccuracies as a consequence of low representation of early age classes in population samplings. To increase early age representation and improve growth modelling, we implemented an approach that used individual growth profile (IGP) data recorded in shells of the Pacific geoduck (Panopea generosa). We compared IGP against SLTA and a combination of both IGP + SLTA data through a multi-model approach for the southernmost known P. generosa population. The most parsimonious model for both IGP and IGP + SLTA data sets was the Schnute model, with L∞ = 127.9 and 122.5 mm, respectively, with the asymptotic phase attained at ∼15 years. For SLTA data alone, the most parsimonious was the Johnson model, with L∞ = 161.6 mm reaching the asymptotic phase at >25 years. In terms of performance, the IGP and IGP + SLTA data sets informed individual growth models with stronger relationships (r2 > 0.9) and higher modelling efficiency (ME > 0.9) than those fitted to SLTA alone (r2 = 0.51; ME = 0.51). The results demonstrate that IGP yields reliable information from relatively few organisms, improves the biological knowledge of the population, and increases the accuracy of parameter estimates for better fishery management.

From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

We study the problem of color-avoiding and color-favored percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links, or is attracted by them. We investigate here regular (mainly directed) lattices with a fractions of links removed (hence the term “diluted”). We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. The method is particularly effective for certain “convex” formulations, but can be extended to arbitrary problems using multi-bit coding. We obtain the phase diagram for some problem related to color-avoiding percolation on directed models. We also show that the interference among colors induces a paradoxical effect in which color-favored percolation is permitted where standard percolation for a single color is impossible.

Testosterone Reduces Growth and Hepatic IGF-1 mRNA in a Female-Larger Lizard, Sceloporus undulatus: Evidence of an Evolutionary Reversal in Growth Regulation

Synopsis Previous research has demonstrated that testosterone (T) can inhibit growth in female-larger species and stimulate growth in male-larger species, but the underlying mechanisms of this regulatory bipotentiality have not been investigated. In this study, we investigated the effects of T on the expression of hepatic insulin-like growth factor-1 (IGF-1) mRNA and circulating IGF-1 hormone in Sceloporus undulatus, a species of lizard in which females grow faster to become larger than males and in which T inhibits growth. Experiments were performed in captivity on mature female and male adults in the asymptotic phase of their growth curve and on actively growing, pre-reproductive juveniles. In adult males, the expression of hepatic IGF-1 mRNA increased following surgical castration and returned to control levels with T replacement; in intact adult females, exogenous T had no effect on IGF-1 mRNA expression. In juveniles, T significantly reduced both growth and the expression of hepatic IGF-1 mRNA to similar extents in intact females and in castrated males. The relative inhibitory effects of T on mRNA expression were greater in juveniles than in adults. Plasma IGF-1 hormone was about four times higher in juveniles than in adults, but T had no significant effect on IGF-1 hormone in either sex or in either age group. Our finding of inhibition of the expression of hepatic IGF-1 mRNA stands in contrast to the stimulatory effects of T in the published body of literature. We attribute our novel finding to our use of a species in which T inhibits rather than stimulates growth. Our findings begin to explain how T has the regulatory bipotentiality to be stimulatory in some species and inhibitory in others, requiring only an evolutionary reversal in the molecular regulation of growth-regulatory genes including IGF-1. Further comparative transcriptomic studies will be required to fully resolve the molecular mechanism of growth inhibition.

Semi-Markov Model and Phase-Merging Scheme of a Multi-Component System with the Group Instantly Replenished Time Reserve

Time redundancy is a method of increasing the reliability and efficiency of the operation of systems for various purposes. A system with time redundancy provides additional time (a time reserve) for restoring characteristics and synchronizing the work of its individual elements. Time reservation is used in production, energy, gas transportation, information, ergonomic systems and some others. In this paper, based on the theory of semi-Markov processes with a common phase space of states, a semi-Markov model of a multicomponent system with a group instantly replenished time reserve is constructed. The reliability characteristics of the system are determined. To approximate the probability and the average time of failure-free operation of the system in conditions of high reliability, asymptotic phase-merging scheme algorithms are used.

Sparsity/undersampling tradeoffs in anisotropic undersampling, with applications in MR imaging/spectroscopy

We study anisotropic undersampling schemes like those used in multi-dimensional magnetic resonance (MR) spectroscopy and imaging, which sample exhaustively in certain time dimensions and randomly in others. Our analysis shows that anisotropic undersampling schemes are equivalent to certain block-diagonal measurement systems. We develop novel exact formulas for the sparsity/undersampling tradeoffs in such measurement systems, assuming uniform sparsity fractions in each column. Our formulas predict finite-$N$ phase transition behavior differing substantially from the well-known asymptotic phase transitions for classical Gaussian undersampling. Extensive empirical work shows that our formulas accurately describe observed finite-$N$ behavior, while the usual formulas based on universality are substantially inaccurate at the moderate $N$ involved in realistic applications. We also vary the anisotropy, keeping the total number of samples fixed, and for each variation we determine the precise sparsity/undersampling tradeoff (phase transition). We show that, other things being equal, the ability to recover a sparse object decreases with an increasing number of exhaustively sampled dimensions.

The WKB(J) Approximation Revisited

This chapter reexamines the WKB(J) approximation and applies it to some simple one-dimensional potentials, with a focus on the case of a triangular barrier. It first considers the connection formulas and proposes an an alternative approach before discussing tunneling from a physical standpoint. It then turns to the case of a triangular barrier and goes on to explore the phase shift, offering some comments on convergence and the transition to classical scattering. It also describes the asymptotic behavior of the Coulomb wave function and revisits the spherical coordinate system. Finally, it finds the WKB(J) approximation with respect to Coulomb scattering and the formal WKB(J) solutions for the time-independent radial Schrödinger equation, and justifies the Langer transformation by showing how the asymptotic phase of the radial WKB(J) wave function is recovered.