Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Compensating for dispersion and nonlinear Kerr effect without phase conjugation

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

Compensating for dispersion and nonlinear Kerr effect without phase conjugation

We propose the use of a dispersive medium with a negative nonlinear refractive-index coefficient as a way to compensate for the dispersion and the nonlinear effects resulting from pulse propagation in an optical fiber. The undoing of pulse interaction might allow for increased bit rates.

Amplifier similariton fiber laser with nonlinear spectral compression

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser’s power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.

New insights in the moderating effect of switching costs on the satisfaction-repurchase behavior link

Existing studies on the role of switching costs (SC) as moderator of the relationship between satisfaction and repurchase behavior are inconclusive. We attempt to explain these inconclusive findings by synthesizing an amplifying and a lock-in effect, and hypothesize a nonlinear moderating effect. In Study 1 (a main study and three replications), we find strong evidence for an inverted u-shaped moderating effect of overall SC. Our results suggest that satisfaction is a particularly important predictor of repurchase behavior in situations characterized by medium-levels of SC. Based on Prospect Theory, Study 2 (a main study and one replication) reveals that this inverted u-shaped moderating effect of SC is stronger for positive (relational and financial) SC than for negative (procedural) SC. We conclude with recommendations for satisfaction management of different customer segments, and describe possibilities to influence customer switching costs in various industries. © 2014 New York University.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

New nonlinear regimes of pulse generation in mode- locked fiber lasers

Mode-locked fiber lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes. The complex interplay among the effects of gain/loss, dispersion and nonlinearity in a fiber cavity can be used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different mode-locking regimes. Major steps forward in pulse energy and peak power performance of passively mode-locked fiber lasers have been made with the recent discovery of new nonlinear regimes of pulse generation, namely, dissipative solitons in all-normal-dispersion cavities and parabolic self-similar pulses (similaritons) in passive and active fibers. Despite substantial research in this field, qualitatively new phenomena are still being discovered. In this talk, we review recent progress in the research on nonlinear mechanisms of pulse generation in passively mode-locked fiber lasers. These include similariton mode-locking, a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on the possibility of achieving various regimes of advanced temporal waveform generation in a mode-locked fiber laser by inclusion of a spectral filter into the laser cavity.

Capacity of nonlinear fibre channels and eigenvalue division multiplexing for optical transmissions

The nonlinear Fourier transform, also known as eigenvalue communications, is a coding, transmission and signal processing technique that makes positive use of the nonlinear Kerr effect in fibre channels. I will discuss recent progress in this field. © 2015 OSA.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Control of the in-cavity dynamics in mode-locked fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral intensity profile, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this talk, we review our recent progress on the realisation of different regimes of pulse generation in passively mode-locked fibre lasers through control of the in-cavity propagation dynamics. We report on the possibility to achieve both parabolic self-similar and triangular pulse shaping in a mode-locked fibre laser via adjustment of the net normal dispersion and integrated gain of the cavity [1]. We also show that careful control of the gain/loss parameters of a net-normal dispersion laser cavity provides the means of achieving switching among Gaussian pulse, dissipative soliton and similariton pulse solutions in the cavity [2,3]. Furthermore, we report on our recent theoretical and experimental studies of pulse shaping by inclusion of an amplitude and phase spectral filter into the cavity of a laser. We numerically demonstrate that a mode-locked fibre laser can operate in dif- ferent pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [4]. An application of technique using a flat-top spectral filter is demonstrated to achieve the direct generation of sinc-shaped optical Nyquist pulses of high quality and of a widely tuneable bandwidth from the laser [5]. We also report on a recently-developed versa- tile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soli- ton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [6]. References: 1. S. Boscolo and S. K. Turitsyn, Phys. Rev. A 85, 043811 (2012). 2. J. Peng et al., Phys. Rev. A 86, 033808 (2012). 3. J. Peng, Opt. Express 24, 3046-3054 (2016). 4. S. Boscolo, C. Finot, H. Karakuzu, and P. Petropoulos, Opt. Lett. 39, 438-441 (2014). 5. S. Boscolo, C. Finot, and S. K. Turitsyn, IEEE Photon. J. 7, 7802008 (2015). 6. J. Peng and S. Boscolo, Sci. Rep. 6, 25995 (2016).

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

Amplitude response of a unilaterally constrained nonlinear micromechanical resonator

Dynamical systems that involve impacts frequently arise in engineering. This Letter reports a study of such a system at microscale that consists of a nonlinear resonator operating with an unilateral impact. The microresonators were fabricated on silicon-on-insulator wafers by using a one-mask process and then characterised by using the capacitively driving and sensing method. Numerical results concerning the dynamics of this vibro-impact system were verified by the experiments. Bifurcation analysis was used to provide a qualitative scenario of the system steady-state solutions as a function of both the amplitude and the frequency of the external driving sinusoidal voltage. The results show that the amplitude of resonant peak is levelled off owing to the impact effect and that the bandwidth of impacting is dependent upon the nonlinearity and the operating conditions.

Effect of dynamical instability on timing jitter in passively mode-locked quantum-dot lasers

We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability in a quantum-dot laser affects timing jitter.

Design and fabrication of a nonlinear micro impact oscillator

In this paper we describe the design and fabrication of a mechanical autonomous impact oscillator with a MEMS resonator as the frequency control element. The design has been developed with scalability to large 2-D arrays of coupled oscillators in mind. The dynamic behaviour of the impact oscillator was numerically studied and it was found that the geometry nonlinearity has an effect on the static pull-in voltage and equilibrium position. The external driving power can alter the frequency of the impact oscillator. The autonomous nature of the oscillator simplifies the complexity of the drive circuitry and is essential for large 2-D arrays.

Mach edges: a critical test of the nonlinear 3rd derivative model for edge-detection

Feature detection is a crucial stage of visual processing. In previous feature-marking experiments we found that peaks in the 3rd derivative of the luminance profile can signify edges where there are no 1st derivative peaks nor 2nd derivative zero-crossings (Wallis and George 'Mach edges' (the edges of Mach bands) were nicely predicted by a new nonlinear model based on 3rd derivative filtering. As a critical test of the model, we now use a new class of stimuli, formed by adding a linear luminance ramp to the blurred triangle waves used previously. The ramp has no effect on the second or higher derivatives, but the nonlinear model predicts a shift from seeing two edges to seeing only one edge as the added ramp gradient increases. In experiment 1, subjects judged whether one or two edges were visible on each trial. In experiment 2, subjects used a cursor to mark perceived edges and bars. The position and polarity of the marked edges were close to model predictions. Both experiments produced the predicted shift from two to one Mach edge, but the shift was less complete than predicted. We conclude that the model is a useful predictor of edge perception, but needs some modification.