Generating functionals for autonomous latching dynamics in attractor relict networks

Coupling local, slowly adapting variables to an attractor network allows to destabilize all attractors, turning them into attractor ruins. The resulting attractor relict network may show ongoing autonomous latching dynamics. We propose to use two generating functionals for the construction of attractor relict networks, a Hopfield energy functional generating a neural attractor network and a functional based on information-theoretical principles, encoding the information content of the neural firing statistics, which induces latching transition from one transiently stable attractor ruin to the next. We investigate the influence of stress, in terms of conflicting optimization targets, on the resulting dynamics. Objective function stress is absent when the target level for the mean of neural activities is identical for the two generating functionals and the resulting latching dynamics is then found to be regular. Objective function stress is present when the respective target activity levels differ, inducing intermittent bursting latching dynamics

Stability and Cycles in a Cobweb Model with Heterogeneous Expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.Bounded rationality, Cobweb model, Flip bifurcation, Neimark-Sacker bifurcation.

Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal posterior surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect

Passivity-based harmonic control through series/parallel damping of an H-bridge rectifier

Nowadays the H-bridge is one of the preferred solutions to connect DC loads or distributed sources to the single-phase grid. The control aims are: sinusoidal grid current with unity power factor and optimal DC voltage regulation capability. These objectives should be satisfied, regardless the conditions of the grid, the DC load/source and the converter nonlinearities. In this paper a passivity-based approach is thoroughly investigated proposing a damping-based solution for the error dynamics. Practical experiments with a real converter validate the analysis.

Market Mood, Adaptive Beliefs and Asset Price Dynamics

Empirical evidence has suggested that, facing different trading strategies and complicated decision, the proportions of agents relying on particular strategies may stay at constant level or vary over time. This paper presents a simple "dynamic market fraction" model of two groups of traders, fundamentalists and trend followers, under a market maker scenario. Market mood and evolutionary adaption are characterized by fixed and adaptive switching fraction among two groups, respectively. Using local stability and bifurcation analysis, as well as numerical simulation, the role played by the key parameters in the market behaviour is examined. Particular attention is payed to the impact of the market fraction, determined by the fixed proportions of confident fundamentalists and trend followers, and by the proportion of adaptively rational agents, who adopt different strategies over time depending on realized profits.

Generating functionals for computational intelligence: the Fisher information as an objective function for self-limiting Hebbian learning rules

Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and explore a new objective function, which allows to obtain plasticity rules for the afferent synaptic weights. The adaption rules are Hebbian, self-limiting, and result from the minimization of the Fisher information with respect to the synaptic flux. We perform a series of simulations examining the behavior of the new learning rules in various circumstances. The vector of synaptic weights aligns with the principal direction of input activities, whenever one is present. A linear discrimination is performed when there are two or more principal directions; directions having bimodal firing-rate distributions, being characterized by a negative excess kurtosis, are preferred. We find robust performance and full homeostatic adaption of the synaptic weights results as a by-product of the synaptic flux minimization. This self-limiting behavior allows for stable online learning for arbitrary durations. The neuron acquires new information when the statistics of input activities is changed at a certain point of the simulation, showing however, a distinct resilience to unlearn previously acquired knowledge. Learning is fast when starting with randomly drawn synaptic weights and substantially slower when the synaptic weights are already fully adapted

Quantitative Assessment of Flame Stability Through Image Processing and Spectral Analysis

This paper experimentally investigates two generalized methods, i.e., a simple universal index and oscillation frequency, for the quantitative assessment of flame stability at fossil-fuel-fired furnaces. The index is proposed to assess the stability of flame in terms of its color, geometry, and luminance. It is designed by combining up to seven characteristic parameters extracted from flame images. The oscillation frequency is derived from the spectral analysis of flame radiation signals. The measurements involved in these two methods do not require prior knowledge about fuel property, burner type, and other operation conditions. They can therefore be easily applied to flame stability assessment without costly and complex adaption. Experiments were carried out on a 9-MW heavy-oil-fired combustion test rig over a wide range of combustion conditions including variations in swirl vane position of the tertiary air, swirl vane position of the secondary air, and the ratio of the primary air to the total air. The impact of these burner parameters on the stability of heavy oil flames is investigated by using the index and oscillation frequency proposed. The experimental results obtained demonstrate the effectiveness of the methods and the importance of maintaining a stable flame for reduced NOx emissions. It is envisaged that such methods can be easily transferred to existing flame closed-circuit television systems and flame failure detectors in power stations for flame stability monitoring