Spiral attractor created by vector solitons

Mode-locked lasers emitting a train of femtosecond pulses called dissipative solitons are an enabling technology for metrology, high-resolution spectroscopy, fibre optic communications, nano-optics and many other fields of science and applications. Recently, the vector nature of dissipative solitons has been exploited to demonstrate mode locked lasing with both locked and rapidly evolving states of polarisation. Here, for an erbium-doped fibre laser mode locked with carbon nanotubes, we demonstrate the first experimental and theoretical evidence of a new class of slowly evolving vector solitons characterized by a double-scroll chaotic polarisation attractor substantially different from Lorenz, Rössler and Ikeda strange attractors. The underlying physics comprises a long time scale coherent coupling of two polarisation modes. The observed phenomena, apart from the fundamental interest, provide a base for advances in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetisation in data storage devices and many other areas. © 2014 CIOMP. All rights reserved.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

The 'moving targets' training algorithm

A simple method for training the dynamical behavior of a neural network is derived. It is applicable to any training problem in discrete-time networks with arbitrary feedback. The method resembles back-propagation in that it is a least-squares, gradient-based optimization method, but the optimization is carried out in the hidden part of state space instead of weight space. A straightforward adaptation of this method to feedforward networks offers an alternative to training by conventional back-propagation. Computational results are presented for simple dynamical training problems, with varied success. The failures appear to arise when the method converges to a chaotic attractor. A patch-up for this problem is proposed. The patch-up involves a technique for implementing inequality constraints which may be of interest in its own right.

Assessing the financial impact of 6-Sigma in an automotive company

This paper reports on an assessment of an ongoing 6-Sigma program conducted within a UK based (US owned) automotive company. It gives an overview of the management of the 6-sigma programme and the 23 in-house methodology used. The analysis given in the paper pays particular focus to the financial impacts that individual projects have had. Three projects are chosen from the hundreds that have been completed and are discussed in detail, including which specific techniques have been used and how financially successful the projects were. Commentary is also given on the effectiveness of the overall program along with a critique of how the implementation of 6-Sigma could be more effectively managed in the future. This discussion particularly focuses upon issues such as: project selection and scoping, financial evaluation and data availability, organisational awareness, commitment and involvement, middle management support, functional variation, and maintaining momentum during the rollout of a lengthy program.

Pentoxifylline and the behaviour of 29-month female mice

The dimethyl-xanthine derivative pentoxifylline (PTX) increases blood flow through capillaries. In elderly humans the drug leads to improvement in a number of imapired neuropsychological parameters. We now report that oral administration to 29-month female mice (C57, black and tan) over six days induced four different patterns of behavioural reponse: (1) consistent improvement in grooming behaviour throughout the six day trial; (2) significant improvement in light/dark zone curiosity and curiosity towards a strange object on day three, which declined but remained significantly above pre-treatment levels at day 6; (3) an improvement in general activity which only becomes detectable on day six; (4) a significant improvement in rod-walking, rearing an shuttle-box crosses on day three which returned to pre-treatment levels by day 6. Age-related deficits in general activity, grooming and curiosity were completely eliminated by the drug - the mean group performance levels attained those seen in 9-12 month individuals of this strain.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Vertraute Fremde? Jens Baggesens und H.C. Andersens Reisen durch Deutschland:Fremdheitswahrnehmung und ihre literarische Gestaltung in "Labyrinten" und "Skyggebilleder"

Jens Baggesen and H.C. Andersen are both aspiring young authors when they set out on their respective journeys to Germany. The literary accounts of their travels - Labyrinten and Skyggebilleder - show how the authors perceive a foreign country, which, despite having a culture closely linked to their own, still contains elements that strike them as being unfamiliar and even bizarre. Their curiosity towards the strange features they encounter is accompanied by a strong desire to reaffirm their own national and cultural identity, forever relying on the comfort of the familiar. When confronted with experiences of strangeness and unfamiliarity that threaten to alienate them, both authors develop similar literary strategies. The poetical programmes that both writers implicitly subscribe to are illustrated in the way they perceive strange and alien elements and are therefore fundamentally and intrinsically interlinked with their aesthetic convictions as writers.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

The idea of the hybrid texts and translation:contact as conflict

Intercultural communication in the global environment frequently involves recourse to translation. This generates new phenomena which, in turn, raise new questions for translation theory and practice. This issue is concerned with the concept of the hybrid text as one of these phenomena. In this introductory chapter, a hybrid text is defined as: „a text that results from a translation process. It shows features that somehow seem ‘out of place'/‘strange'/‘unusual' for the receiving culture, i.e. the target culture”. It is important, however, to differentiate between the true hybrid, which is the result of positive authorial and/or translatorial decisions, and the inadequate text which exhibits features of translationese, resulting from a lack of competence. Textual, contextual and social features of hybrid texts are postulated (see discussion paper). These are the object of critical reflection in sub-sequent chapters, in relation to different genres. The potential of the hybrid text for translation research is explored.

Vector solitons in mode locked fibre lasers

We overview our recent results on polarisation dynamics of vector solitons in erbium doped fibre laser mode locked with carbon nanotubes. Our experimental and theoretical study revealed new families of vector solitons for fundamental and bound-state soliton operations. The observed scenario of the evolution of the states of polarisation (SOPs) on the Poincare sphere includes fast polarisation switching between two and three SOPs along with slow SOP evolution on a double scroll chaotic attractor. The underlying physics presents an interplay between effects of birefringence of the laser cavity and light induced anisotropy caused by polarisation hole burning. © 2014 IEEE.

Editorial

The year so far has been a slow start for many businesses, but at least we have not seen the collapse of as many businesses that we were seeing around two years ago. We are, however, still well and truly in the midst of a global recession. Interest rates are still at an all time low, UK house prices seem to be showing little signs of increase (except in London where everyone still seems to want to live!) and for the ardent shopper there are bargains to be had everywhere. It seems strange that prices on the high street do not seem to have increased in over ten years. Mobile phones, DVD players even furniture seems to be cheaper than they used to be. Whist much of this is down to cheaper manufacturing and the rest could probably be explained by competition within the market place. Does this mean that quality suffered too? Now that we live in a world when if a television is not working it is thrown away and replaced. There was a time when you would take it to some odd looking man that your father would know who could fix it for you. (I remember our local television fix-it man, with his thick rimmed bifocal spectacles and a poor comb-over; he had cardboard boxes full of resistors and electrical wires on the floor of his front room that smelt of soldering irons!) Is this consumerism at an extreme or has this move to disposability made us a better society? Before you think these are just ramblings there is a point to this. According to latest global figures of contact lens sales the vast majority of contact lenses fitted around the world are daily, fortnightly or monthly disposable hydrogel lenses. Certainly in the UK over 90% of lenses are disposable (with daily disposables being the most popular, having a market share of over 50%). This begs the question – is this a good thing? Maybe more importantly, do our patients benefit? I think it is worth reminding ourselves why we went down the disposability route with contact lenses in the first place, and unlike electrical goods it was not just so we did not have to take them for repair! There are the obvious advantages of overcoming problems of breakage and tearing of lenses and the lens deterioration with age. The lenses are less likely to be contaminated and the disinfection is either easier or not required at all (in the case of daily disposable lenses). Probably the landmark paper in the field was the work more commonly known as the ‘Gothenburg Study’. The paper, entitled ‘Strategies for minimizing the Ocular Effects of Extended Contact Lens Wear’ published in the American Journal of Optometry in 1987 (volume 64, pages 781-789) by Holden, B.A., Swarbrick, H.A., Sweeney, D.F., Ho, A., Efron, N., Vannas, A., Nilsson, K.T. They suggested that contact lens induced ocular effects were minimised by: •More frequently removed contact lenses •More regularly replaced contact lenses •A lens that was more mobile on the eye (to allow better removal of debris) •Better flow of oxygen through the lens All of these issues seem to be solved with disposability, except the oxygen issue which has been solved with the advent of silicone hydrogel materials. Newer issues have arisen and most can be solved in practice by the eye care practitioner. The emphasis now seems to be on making lenses more comfortable. The problems of contact lens related dry eyes symptoms seem to be ever present and maybe this would explain why in the UK we have a pretty constant contact lens wearing population of just over three million but every year we have over a million dropouts! That means we must be attracting a million new wearers every year (well done to the marketing departments!) but we are also losing a million wearers every year. We certainly are not losing them all to the refractive surgery clinics. We know that almost anyone can now wear a contact lens and we know that some lenses will solve problems of sharper vision, some will aid comfort, and some will be useful for patients with dry eyes. So if we still have so many dropouts then we must be doing something wrong! I think the take home message has to be ‘must try harder’! I must end with an apology for two errors in my editorial of issue 1 earlier this year. Firstly there was a typo in the first sentence; I meant to state that it was 40 years not 30 years since the first commercial soft lens was available in the UK. The second error was one that I was unaware of until colleagues Geoff Wilson (Birmingham, UK) and Tim Bowden (London, UK) wrote to me to explain that soft lenses were actually available in the UK before 1971 (please see their ‘Letters to the Editor’ in this issue). I am grateful to both of them for correcting the mistake.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.