Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network

In this study, an artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the short-term $x(t+6)$. The performance prediction was evaluated and compared with another studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute uncertainties of predictions for noisy Mackey--Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level ($\sigma_{N}$) from 0.01 to 0.1.Comment: 11 pages, 8 figure

Metric preheating and limitations of linearized gravity

Recently it has become clear that the resonant amplification of quantum field fluctuations at preheating must be accompanied by resonant amplification of scalar metric perturbations, since the two are united by Einstein's equations. Furthermore, this "metric preheating" enhances particle production and leads to gravitational rescattering effects even at linear order. In multi-field models with strong preheating (q \gg 1), metric perturbations are driven nonlinear, with the strongest amplification typically on super-Hubble scales (k \to 0). This amplification is causal, being due to the super- Hubble coherence of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications at all scales - from the large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the (q,k) parameter space in a two-field model, and introduce the time to nonlinearity, t_{nl}, as the timescale for the breakdown of the linearized Einstein equations. Backreaction effects are expected to shut down the linear resonances, but cannot remove the existing amplification, which threatens the viability of strong preheating when confronted with the CMB. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. Finally we rank known classes of inflation from strongest (chaotic and strongly coupled hybrid inflation) to weakest (hidden sector, warm inflation) in terms of the distortion of the primordial spectrum due to these resonances in preheating.Comment: 31 pages, 16 figures, Revtex. Final version. Nuclear Physics B (in press

Chaos, Fractals and Inflation

In order to draw out the essential behavior of the universe, investigations of early universe cosmology often reduce the complex system to a simple integrable system. Inflationary models are of this kind as they focus on simple scalar field scenarios with correspondingly simple dynamics. However, we can be assured that the universe is crowded with many interacting fields of which the inflaton is but one. As we describe, the nonlinear nature of these interactions can result in a complex, chaotic evolution of the universe. Here we illustrate how chaotic effects can arise even in basic models such as homogeneous, isotropic universes with two scalar fields. We find inflating universes which act as attractors in the space of initial conditions. These universes display chaotic transients in their early evolution. The chaotic character is reflected by the fractal border to the basin of attraction. The broader implications are likely to be felt in the process of reheating as well as in the nature of the cosmic background radiation.Comment: 16 pages, RevTeX. See published version for fig

Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.Comment: Published in Nature Photonic

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms