Signal processing for molecular and cellular biological physics:an emerging field

Recent advances in our ability to watch the molecular and cellular processes of life in action-such as atomic force microscopy, optical tweezers and Forster fluorescence resonance energy transfer-raise challenges for digital signal processing (DSP) of the resulting experimental data. This article explores the unique properties of such biophysical time series that set them apart from other signals, such as the prevalence of abrupt jumps and steps, multi-modal distributions and autocorrelated noise. It exposes the problems with classical linear DSP algorithms applied to this kind of data, and describes new nonlinear and non-Gaussian algorithms that are able to extract information that is of direct relevance to biological physicists. It is argued that these new methods applied in this context typify the nascent field of biophysical DSP. Practical experimental examples are supplied.

Pattern recognition analyses of brain activation elicited by happy and neutral faces in unipolar and bipolar depression

Objectives: Recently, pattern recognition approaches have been used to classify patterns of brain activity elicited by sensory or cognitive processes. In the clinical context, these approaches have been mainly applied to classify groups of individuals based on structural magnetic resonance imaging (MRI) data. Only a few studies have applied similar methods to functional MRI (fMRI) data. Methods: We used a novel analytic framework to examine the extent to which unipolar and bipolar depressed individuals differed on discrimination between patterns of neural activity for happy and neutral faces. We used data from 18 currently depressed individuals with bipolar I disorder (BD) and 18 currently depressed individuals with recurrent unipolar depression (UD), matched on depression severity, age, and illness duration, and 18 age- and gender ratio-matched healthy comparison subjects (HC). fMRI data were analyzed using a general linear model and Gaussian process classifiers. Results: The accuracy for discriminating between patterns of neural activity for happy versus neutral faces overall was lower in both patient groups relative to HC. The predictive probabilities for intense and mild happy faces were higher in HC than in BD, and for mild happy faces were higher in HC than UD (all p < 0.001). Interestingly, the predictive probability for intense happy faces was significantly higher in UD than BD (p = 0.03). Conclusions: These results indicate that patterns of whole-brain neural activity to intense happy faces were significantly less distinct from those for neutral faces in BD than in either HC or UD. These findings indicate that pattern recognition approaches can be used to identify abnormal brain activity patterns in patient populations and have promising clinical utility as techniques that can help to discriminate between patients with different psychiatric illnesses.

Examination of the predictive value of structural magnetic resonance scans in bipolar disorder:a pattern classification approach

Background - Bipolar disorder (BD) is one of the leading causes of disability worldwide. Patients are further disadvantaged by delays in accurate diagnosis ranging between 5 and 10 years. We applied Gaussian process classifiers (GPCs) to structural magnetic resonance imaging (sMRI) data to evaluate the feasibility of using pattern recognition techniques for the diagnostic classification of patients with BD. Method - GPCs were applied to gray (GM) and white matter (WM) sMRI data derived from two independent samples of patients with BD (cohort 1: n = 26; cohort 2: n = 14). Within each cohort patients were matched on age, sex and IQ to an equal number of healthy controls. Results - The diagnostic accuracy of the GPC for GM was 73% in cohort 1 and 72% in cohort 2; the sensitivity and specificity of the GM classification were respectively 69% and 77% in cohort 1 and 64% and 99% in cohort 2. The diagnostic accuracy of the GPC for WM was 69% in cohort 1 and 78% in cohort 2; the sensitivity and specificity of the WM classification were both 69% in cohort 1 and 71% and 86% respectively in cohort 2. In both samples, GM and WM clusters discriminating between patients and controls were localized within cortical and subcortical structures implicated in BD. Conclusions - Our results demonstrate the predictive value of neuroanatomical data in discriminating patients with BD from healthy individuals. The overlap between discriminative networks and regions implicated in the pathophysiology of BD supports the biological plausibility of the classifiers.

Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions. © 2005 Optical Society of America.

Modeling of spectral and statistical properties of a random distributed feedback fiber laser

For the first time we report full numerical NLSE-based modeling of generation properties of random distributed feedback fiber laser based on Rayleigh scattering. The model which takes into account the random backscattering via its average strength only describes well power and spectral properties of random DFB fiber lasers. The influence of dispersion and nonlinearity on spectral and statistical properties is investigated. The evidence of non-gaussian intensity statistics is found. © 2013 Optical Society of America.

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Sub-critical regime of femtosecond inscription

We apply well known nonlinear diffraction theory governing focusing of a powerful light beam of arbitrary shape in medium with Kerr nonlinearity to the analysis of femtosecond (fs) laser processing of dielectric in sub-critical (input power less than the critical power of selffocusing) regime. Simple analytical expressions are derived for the input beam power and spatial focusing parameter (numerical aperture) that are required for achieving an inscription threshold. Application of non-Gaussian laser beams for better controlled fs inscription at higher powers is also discussed. © 2007 Optical Society of America.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Probabilistic topographic information visualisation

The focus of this thesis is the extension of topographic visualisation mappings to allow for the incorporation of uncertainty. Few visualisation algorithms in the literature are capable of mapping uncertain data with fewer able to represent observation uncertainties in visualisations. As such, modifications are made to NeuroScale, Locally Linear Embedding, Isomap and Laplacian Eigenmaps to incorporate uncertainty in the observation and visualisation spaces. The proposed mappings are then called Normally-distributed NeuroScale (N-NS), T-distributed NeuroScale (T-NS), Probabilistic LLE (PLLE), Probabilistic Isomap (PIso) and Probabilistic Weighted Neighbourhood Mapping (PWNM). These algorithms generate a probabilistic visualisation space with each latent visualised point transformed to a multivariate Gaussian or T-distribution, using a feed-forward RBF network. Two types of uncertainty are then characterised dependent on the data and mapping procedure. Data dependent uncertainty is the inherent observation uncertainty. Whereas, mapping uncertainty is defined by the Fisher Information of a visualised distribution. This indicates how well the data has been interpolated, offering a level of ‘surprise’ for each observation. These new probabilistic mappings are tested on three datasets of vectorial observations and three datasets of real world time series observations for anomaly detection. In order to visualise the time series data, a method for analysing observed signals and noise distributions, Residual Modelling, is introduced. The performance of the new algorithms on the tested datasets is compared qualitatively with the latent space generated by the Gaussian Process Latent Variable Model (GPLVM). A quantitative comparison using existing evaluation measures from the literature allows performance of each mapping function to be compared. Finally, the mapping uncertainty measure is combined with NeuroScale to build a deep learning classifier, the Cascading RBF. This new structure is tested on the MNist dataset achieving world record performance whilst avoiding the flaws seen in other Deep Learning Machines.

A lower bound on the per soliton capacity of the nonlinear optical fibre channel

A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.

Improved data visualisation through multiple dissimilarity modelling

Popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically Euclidean, for instance Metric Multidimensional Scaling, t-distributed Stochastic Neighbour Embedding and the Gaussian Process Latent Variable Model. It is well known that this assumption does not hold for most datasets and often high-dimensional data sits upon a manifold of unknown global geometry. We present a method for improving the manifold charting process, coupled with Elastic MDS, such that we no longer assume that the manifold is Euclidean, or of any particular structure. We draw on the benefits of different dissimilarity measures allowing for the relative responsibilities, under a linear combination, to drive the visualisation process.

Development and validation of a computationally efficient pseudo 3D model for planar SOFC integrated with a heating furnace

Efficient numerical models facilitate the study and design of solid oxide fuel cells (SOFCs), stacks, and systems. Whilst the accuracy and reliability of the computed results are usually sought by researchers, the corresponding modelling complexities could result in practical difficulties regarding the implementation flexibility and computational costs. The main objective of this article is to adapt a simple but viable numerical tool for evaluation of our experimental rig. Accordingly, a model for a multi-layer SOFC surrounded by a constant temperature furnace is presented, trained and validated against experimental data. The model consists of a four-layer structure including stand, two interconnects, and PEN (Positive electrode-Electrolyte-Negative electrode); each being approximated by a lumped parameter model. The heating process through the surrounding chamber is also considered. We used a set of V-I characteristics data for parameter adjustment followed by model verification against two independent sets of data. The model results show a good agreement with practical data, offering a significant improvement compared to reduced models in which the impact of external heat loss is neglected. Furthermore, thermal analysis for adiabatic and non-adiabatic process is carried out to capture the thermal behaviour of a single cell followed by a polarisation loss assessment. Finally, model-based design of experiment is demonstrated for a case study.

Towards person-centered neuroimaging markers for resilience and vulnerability in Bipolar Disorder

Improved clinical care for Bipolar Disorder (BD) relies on the identification of diagnostic markers that can reliably detect disease-related signals in clinically heterogeneous populations. At the very least, diagnostic markers should be able to differentiate patients with BD from healthy individuals and from individuals at familial risk for BD who either remain well or develop other psychopathology, most commonly Major Depressive Disorder (MDD). These issues are particularly pertinent to the development of translational applications of neuroimaging as they represent challenges for which clinical observation alone is insufficient. We therefore applied pattern classification to task-based functional magnetic resonance imaging (fMRI) data of the n-back working memory task, to test their predictive value in differentiating patients with BD (n=30) from healthy individuals (n=30) and from patients' relatives who were either diagnosed with MDD (n=30) or were free of any personal lifetime history of psychopathology (n=30). Diagnostic stability in these groups was confirmed with 4-year prospective follow-up. Task-based activation patterns from the fMRI data were analyzed with Gaussian Process Classifiers (GPC), a machine learning approach to detecting multivariate patterns in neuroimaging datasets. Consistent significant classification results were only obtained using data from the 3-back versus 0-back contrast. Using contrast, patients with BD were correctly classified compared to unrelated healthy individuals with an accuracy of 83.5%, sensitivity of 84.6% and specificity of 92.3%. Classification accuracy, sensitivity and specificity when comparing patients with BD to their relatives with MDD, were respectively 73.1%, 53.9% and 94.5%. Classification accuracy, sensitivity and specificity when comparing patients with BD to their healthy relatives were respectively 81.8%, 72.7% and 90.9%. We show that significant individual classification can be achieved using whole brain pattern analysis of task-based working memory fMRI data. The high accuracy and specificity achieved by all three classifiers suggest that multivariate pattern recognition analyses can aid clinicians in the clinical care of BD in situations of true clinical uncertainty regarding the diagnosis and prognosis.

Upper and lower bounds on the learning curve for Gaussian processes

In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Gaussian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.