The (n+1)/2 rule for dealiasing in the split-step Fourier methods for n-wave interactions

The aim of this letter is to demonstrate that complete removal of spectral aliasing occurring due to finite numerical bandwidth used in the split-step Fourier simulations of nonlinear interactions of optical waves can be achieved by enlarging each dimension of the spectral domain by a factor (n+1)/2, where n is the number of interacting waves. Alternatively, when using low-pass filtering for dealiasing this amounts to the need for filtering a 2/(n+1) fraction of each spectral dimension.

Probing three-way interactions in moderated multiple regression:Development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research. Copyright 2006 by the American Psychological Association.

Septin6 and Septin7 GTP binding proteins regulate AP-3- and ESCRT-dependent multivesicular body biogenesis

Septins (SEPTs) form a family of GTP-binding proteins implicated in cytoskeleton and membrane organization, cell division and host/pathogen interactions. The precise function of many family members remains elusive. We show that SEPT6 and SEPT7 complexes bound to F-actin regulate protein sorting during multivesicular body (MVB) biogenesis. These complexes bind AP-3, an adapter complex sorting cargos destined to remain in outer membranes of maturing endosomes, modulate AP-3 membrane interactions and the motility of AP-3-positive endosomes. These SEPT-AP interactions also influence the membrane interaction of ESCRT (endosomal-sorting complex required for transport)-I, which selects ubiquitinated cargos for degradation inside MVBs. Whereas our findings demonstrate that SEPT6 and SEPT7 function in the spatial, temporal organization of AP-3- and ESCRT-coated membrane domains, they uncover an unsuspected coordination of these sorting machineries during MVB biogenesis. This requires the E3 ubiquitin ligase LRSAM1, an AP-3 interactor regulating ESCRT-I sorting activity and whose mutations are linked with Charcot-Marie-Tooth neuropathies.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Novel peptide antagonists of adrenomedullin and calcitonin gene-related peptide receptors:identification, pharmacological characterization, and interactions with position 74 in receptor activity-modifying protein 1/3

Human adrenomedullin (AM) is a 52-amino acid peptide belonging to the calcitonin peptide family, which also includes calcitonin gene-related peptide (CGRP) and AM2. The two AM receptors, AM(1) and AM(2), are calcitonin receptor-like receptor (CL)/receptor activity-modifying protein (RAMP) (RAMP2 and RAMP3, respectively) heterodimers. CGRP receptors comprise CL/RAMP1. The only human AM receptor antagonist (AM(22-52)) is a truncated form of AM; it has low affinity and is only weakly selective for AM(1) over AM(2) receptors. To develop novel AM receptor antagonists, we explored the importance of different regions of AM in interactions with AM(1), AM(2), and CGRP receptors. AM(22-52) was the framework for generating further AM fragments (AM(26-52) and AM(30-52)), novel AM/alphaCGRP chimeras (C1-C5 and C9), and AM/AM(2) chimeras (C6-C8). cAMP assays were used to screen the antagonists at all receptors to determine their affinity and selectivity. Circular dichroism spectroscopy was used to investigate the secondary structures of AM and its related peptides. The data indicate that the structures of AM, AM2, and alphaCGRP differ from one another. Our chimeric approach enabled the identification of two nonselective high-affinity antagonists of AM(1), AM(2), and CGRP receptors (C2 and C6), one high-affinity antagonist of AM(2) receptors (C7), and a weak antagonist selective for the CGRP receptor (C5). By use of receptor mutagenesis, we also determined that the C-terminal nine amino acids of AM seem to be responsible for its interaction with Glu74 of RAMP3. We provide new information on the structure-activity relationship of AM, alphaCGRP, and AM2 and how AM interacts with CGRP and AM(2) receptors.

Wave kinetics of random fibre lasers

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).