Modelling of non-stationary processes using radial basis function networks

This paper reports preliminary progress on a principled approach to modelling nonstationary phenomena using neural networks. We are concerned with both parameter and model order complexity estimation. The basic methodology assumes a Bayesian foundation. However to allow the construction of pragmatic models, successive approximations have to be made to permit computational tractibility. The lowest order corresponds to the (Extended) Kalman filter approach to parameter estimation which has already been applied to neural networks. We illustrate some of the deficiencies of the existing approaches and discuss our preliminary generalisations, by considering the application to nonstationary time series.

Tracking of non-stationary time-series using resource allocating RBF networks

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Using electricity load data and training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise and forgetting factors for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. We also find that a recently-proposed alternative novelty criterion, found to be more robust in stationary environments, does not fare so well in the non-stationary case due to the need for filter adaptability during training.

A Bayesian formulation of search, control and the exploration/exploitation trade-off

A new approach to optimisation is introduced based on a precise probabilistic statement of what is ideally required of an optimisation method. It is convenient to express the formalism in terms of the control of a stationary environment. This leads to an objective function for the controller which unifies the objectives of exploration and exploitation, thereby providing a quantitative principle for managing this trade-off. This is demonstrated using a variant of the multi-armed bandit problem. This approach opens new possibilities for optimisation algorithms, particularly by using neural network or other adaptive methods for the adaptive controller. It also opens possibilities for deepening understanding of existing methods. The realisation of these possibilities requires research into practical approximations of the exact formalism.

GLM-beamformer method demonstrates stationary field, alpha ERD and gamma ERS co-localisation with fMRI BOLD response in visual cortex

Recently, we introduced a new 'GLM-beamformer' technique for MEG analysis that enables accurate localisation of both phase-locked and non-phase-locked neuromagnetic effects, and their representation as statistical parametric maps (SPMs). This provides a useful framework for comparison of the full range of MEG responses with fMRI BOLD results. This paper reports a 'proof of principle' study using a simple visual paradigm (static checkerboard). The five subjects each underwent both MEG and fMRI paradigms. We demonstrate, for the first time, the presence of a sustained (DC) field in the visual cortex, and its co-localisation with the visual BOLD response. The GLM-beamformer analysis method is also used to investigate the main non-phase-locked oscillatory effects: an event-related desynchronisation (ERD) in the alpha band (8-13 Hz) and an event-related synchronisation (ERS) in the gamma band (55-70 Hz). We show, using SPMs and virtual electrode traces, the spatio-temporal covariance of these effects with the visual BOLD response. Comparisons between MEG and fMRI data sets generally focus on the relationship between the BOLD response and the transient evoked response. Here, we show that the stationary field and changes in oscillatory power are also important contributors to the BOLD response, and should be included in future studies on the relationship between neuronal activation and the haemodynamic response. © 2005 Elsevier Inc. All rights reserved.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Stationary scattering from a nonlinear network

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.

A procedure for the reconstruction of a stochastic stationary temperature field

An iterative procedure is proposed for the reconstruction of a temperature field from a linear stationary heat equation with stochastic coefficients, and stochastic Cauchy data given on a part of the boundary of a bounded domain. In each step, a series of mixed well-posed boundary-value problems are solved for the stochastic heat operator and its adjoint. Well-posedness of these problems is shown to hold and convergence in the mean of the procedure is proved. A discretized version of this procedure, based on a Monte Carlo Galerkin finite-element method, suitable for numerical implementation is discussed. It is demonstrated that the solution to the discretized problem converges to the continuous as the mesh size tends to zero.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

Investigation into the performance and emissions of a stationary diesel engine fuelled by sewage sludge intermediate pyrolysis oil and biodiesel blends

This paper studies the characteristics of blends of biodiesel and a new type of SSPO (sewage sludge derived intermediate pyrolysis oil) in various ratios, and evaluates the application of such blends in an unmodified Lister diesel engine. The engine performance and exhaust emissions were investigated and compared to those of diesel and biodiesel. The engine injectors were inspected and tested after the experiment. The SSPO-biodiesel blends were found to have comparable heating values to biodiesel, but relatively high acidity and carbon residue. The diesel engine has operated with a 30/70 SSPO-biodiesel blend and a 50/50 blend for up to 10h and there was no apparent deterioration in operation observed. It is concluded that with 30% SSPO, the engine gives better overall performance and fuel consumption than with 50% SSPO. The exhaust temperatures of 30% SSPO and 50% SSPO are similar, but 30% SSPO gives relatively lower NO emission than 50% SSPO. The CO and smoke emissions are lower with 50% SSPO than with 30% SSPO. The injectors of the engine operated with SSPO blends were found to have heavy carbon deposition and noticeably reduced opening pressure, which may lead to deteriorated engine performance and exhaust emissions in extended operation. © 2013 Elsevier Ltd.

Reconstruction of a stationary flow from boundary data using iterative methods

In this paper, three iterative procedures (Landweber-Fridman, conjugate gradient and minimal error methods) for obtaining a stable solution to the Cauchy problem in slow viscous flows are presented and compared. A section is devoted to the numerical investigations of these algorithms. There, we use the boundary element method together with efficient stopping criteria for ceasing the iteration process in order to obtain stable solutions.

An iterative method for the reconstruction of a stationary flow

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007

An alternating method for the stationary Stokes system

An alternating procedure for solving a Cauchy problem for the stationary Stokes system is presented. A convergence proof of this procedure and numerical results are included.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.