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.

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.

Objective analysis of toric intraocular lens rotation and centration

PURPOSE: To assess the repeatability of an objective image analysis technique to determine intraocular lens (IOL) rotation and centration. SETTING: Six ophthalmology clinics across Europe. METHODS: One-hundred seven patients implanted with Akreos AO aspheric IOLs with orientation marks were imaged. Image quality was rated by a masked observer. The axis of rotation was determined from a line bisecting the IOL orientation marks. This was normalized for rotation of the eye between visits using the axis bisecting 2 consistent conjunctival vessels or iris features. The center of ovals overlaid to circumscribe the IOL optic edge and the pupil or limbus were compared to determine IOL centration. Intrasession repeatability was assessed in 40 eyes and the variability of repeated analysis examined. RESULTS: Intrasession rotational stability of the IOL was ±0.79 degrees (SD) and centration was ±0.10 mm horizontally and ±0.10 mm vertically. Repeated analysis variability of the same image was ±0.70 degrees for rotation and ±0.20 mm horizontally and ±0.31 mm vertically for centration. Eye rotation (absolute) between visits was 2.23 ± 1.84 degrees (10%>5 degrees rotation) using one set of consistent conjunctival vessels or iris features and 2.03 ± 1.66 degrees (7%>5 degrees rotation) using the average of 2 sets (P =.13). Poorer image quality resulted in larger apparent absolute IOL rotation (r =-0.45,P<.001). CONCLUSIONS: Objective analysis of digital retroillumination images allows sensitive assessment of IOL rotation and centration stability. Eye rotation between images can lead to significant errors if not taken into account. Image quality is important to analysis accuracy.

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).

Neuromagnetic evoked responses to complex motions are greatest for expansion

We analysed evoked magnetic responses to moving random dot stimuli, initially using a 19-channel magnetoencephalography (MEG) system, and subsequently using a 151-channel MEG system. Random dot displays were used to construct complex motion sequences, which we refer to as expansion, contraction, deformation, and rotation. We also investigated lateral translation and a condition in which the directions of the dots were randomised. In all stimulus conditions, the dots were first stationary, then traveled for a brief period (317s or 542 ms), and were then stationary again. In all conditions, evoked magnetic responses were observed with a widespread bilateral distribution over the observers' heads. Initial recordings revealed a substantially larger evoked magnetic response to the expansion condition than the other conditions. In a revised study, we used a 151-channel MEG system and two stimulus diameters (9.3 and 48 deg), the smaller comparable with the first experiment. The responses were analysed using a nonparametric approach and confirmed our initial observations. In a third study, speed gradients were removed and a new design permitted direct comparisons between motion conditions. The results from all three experiments are consistent with the greater ecological validity of the expansion stimulus. © 2004 Elsevier B.V. All rights reserved.

Independent detectors for expansion and rotation, and for orthogonal components of deformation

It is well known that optic flow - the smooth transformation of the retinal image experienced by a moving observer - contains valuable information about the three-dimensional layout of the environment. From psychophysical and neurophysiological experiments, specialised mechanisms responsive to components of optic flow (sometimes called complex motion) such as expansion and rotation have been inferred. However, it remains unclear (a) whether the visual system has mechanisms for processing the component of deformation and (b) whether there are multiple mechanisms that function independently from each other. Here, we investigate these issues using random-dot patterns and a forced-choice subthreshold summation technique. In experiment 1, we manipulated the size of a test region that was permitted to contain signal and found substantial spatial summation for signal components of translation, expansion, rotation, and deformation embedded in noise. In experiment 2, little or no summation was found for the superposition of orthogonal pairs of complex motion patterns (eg expansion and rotation), consistent with probability summation between pairs of independent detectors. Our results suggest that optic-flow components are detected by mechanisms that are specialised for particular patterns of complex motion.

21-residue peptide's dynamics at and between elementary structural transitions

Elementary conformational changes of the backbone of a 21-residue peptide A5(A3RA)3A are studied using molecular dynamics simulations in explicit water. The processes of the conformational transitions and the regimes of stationary fluctuations between them are investigated using minimal perturbations of the system. The perturbations consist of a few degrees rotation of the velocity of one of the systems' atoms and keep the system on the same energy surface. It is found that (i) the system dynamics is insignificantly changed by the perturbations in the regimes between the transitions; (ii) it is very sensitive to the perturbations just before the transitions that prevents the peptide from making the transitions; and (iii) the perturbation of any atom of the system, including distant water molecules is equally effective in preventing the transition. The latter implies strongly collective dynamics of the peptide and water during the transitions.

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.

Continous annular chromatography for the separation of carbohydrate mixtures

The continuous separation of beet molasses resulting in a sucrose rich product and a non-sugar waste product was carried out using a rotating annular chromatograph. The annulus was 12 mm wide and 1.4 m long and was packed with a sodium charged 5.5% cross-linked polystyrene ion exchange resin. Separation was achieved by the simultaneous mechanisms of ion exclusion, size exclusion and partition chromatography. The entire packed bed was slowly rotated while beet molasses was fed continuously through a stationary feed nozzle to the top of the bed. Each molasses constituent having a different relative affinity for the packing and the deionised water mobile phase describes a characteristic helical path as it progresses from the stationary feed point to the bottom of the rotating bed. Each solute then elutes from the annulus at a different angular distance from the feed and separation of the multicomponent mixture is thereby achieved. When a 35% w/w sucrose beet molasses feed was used the throughput achievable was 45.1 kg sucrose m~3 resin h"1. In addition to beet molasses separation other carbohydrate mixtures were separated. In particular the separation of glucose and fructose by Ligand exchange chromatography on a calcium charged ion exchange bed was carried out. The effects of flowrates, concentration, rotation rate, temperature and particle size on resolution and dilution of constituents in the mixtures to be separated were studied. A small test rig was designed and built to determine the cause of liquid maldistribution around the annulus. The problem was caused by the porous bed support media becoming clogged with fines being introduced by eluent flows and off the resin. An outer ring was constructed to house the bed support which could be quickly replaced with the onset of maldistribution. The computer simulation of the operation of the rotating annular chromatograph has been carried out successfully.