Arifah Bahar

Spectral Estimation of Nonstationary EEG Using Particle Filtering With Application to Event-Related Desynchronization (ERD)

This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.

Enhanced compact artificial bee colony

Challenges in many real-world optimization problems arise from limited hardware availability, particularly when the optimization must be performed on a device whose hardware is highly restricted due to cost or space. This paper proposes a new algorithm, namely Enhanced compact Artificial Bee Colony (EcABC) to address this class of optimization problems. The algorithm benefits from the search logic of the Artificial Bee Colony (ABC) algorithm, and similar to other compact algorithms, it does not store the actual population of tentative solutions. Instead, EcABC employs a novel probabilistic representation of the population that is introduced in this paper. The proposed algorithm has been tested on a set of benchmark functions from the CEC2013 benchmark suite, and compared against a number of algorithms including modern compact algorithms, recent population-based ABC variants and some advanced meta-heuristics. Numerical results demonstrate that EcABC significantly outperforms other state of the art compact algorithms. In addition, simulations also indicate that the proposed algorithm shows a comparative performance when compared against its population-based versions.

Modelling contaminant transport for pumping wells in riverbank filtration systems.

Analytical study of the influence of both the pumping well discharge rate and pumping time on contaminant transport and attenuation is significant for hydrological and environmental science applications. This article provides an analytical solution for investigating the influence of both pumping time and travelling time together for one-dimensional contaminant transport in riverbank filtration systems by using the Greens function approach. The basic aim of the model is to understand how the pumping time and pumping rate, which control the travelling time, can affect the contaminant concentration in riverbank filtration systems. Results of analytical solutions are compared with the results obtained using a MODFLOW numerical model. Graphically, it is found that both analytical and numerical solutions have almost the same behaviour. Additionally, the graphs indicate that any increase in the pumping rate or simulation pumping time should increase the contamination in groundwater. The results from the proposed analytical model are well matched with the data collected from a riverbank filtration site in France. After this validation, the model is then applied to the first pilot project of a riverbank filtration system conducted in Malaysia. Sensitivity analysis results highlight the importance of degradation rates of contaminants on groundwater quality, for which higher utilization rates lead to the faster consumption of pollutants.

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.

Modeling and estimation of single-trial event-related potentials using partially observed diffusion processes

This paper proposes a new modeling framework for estimating single-trial event-related potentials (ERPs). Existing studies based on state-space approach use discrete-time random-walk models. We propose to use continuous-time partially observed diffusion process which is more natural and appropriate to describe the continuous dynamics underlying ERPs, discretely observed in noise as single-trials. Moreover, the flexibility of the continuous-time model being specified and analyzed independently of observation intervals, enables a more efficient handling of irregularly or variably sampled ERPs than its discrete-time counterpart which is fixed to a particular interval. We consider the Ornstein-Uhlenbeck (OU) process for the inter-trial parameter dynamics and further propose a nonlinear process of Cox, Ingersoll & Ross (CIR) with a heavy-tailed density to better capture the abrupt changes. We also incorporate a single-trial trend component using the mean-reversion variant, and a stochastic volatility noise process. The proposed method is applied to analysis of auditory brainstem responses (ABRs). Simulation shows that both diffusions give satisfactory tracking performance, particularly of the abrupt ERP parameter variations by the CIR process. Evaluation on real ABR data across different subjects, stimulus intensities and hearing conditions demonstrates the superiority of our method in extracting the latent single-trial dynamics with significantly improved SNR, and in detecting the wave V which is critical for diagnosis of hearing loss. Estimation results on data with variable sampling frequencies and missing single-trials show that the continuous-time diffusion model can capture more accurately the inter-trial dynamics between varying observation intervals, compared to the discrete-time model. Continuous-time partially observed diffusion modeling of single-trial ERPs.Improved modeling of hidden continuous dynamics and irregularly spaced ERPs.Ornstein-Uhlenbeck and Cox, Ingersoll & Ross process (to capture abrupt changes).Incorporate single-trial trend component and stochastic volatility noise process.Better single-trial estimates of auditory brainstem responses & wave V detection.

Artifact Removal from Single-Trial ERPs using Non-Gaussian Stochastic Volatility Models and Particle Filter

This paper considers improved modeling of artifactual noise for denoising of single-trial event-related potentials (ERPs) by state-space approach. Instead of the inadequate constant variance models used in existing studies, we propose to use stochastic volatility (SV) models to better describe the time-varying volatility in real ERP noise sources. We further propose a class of non-Gaussian SV models to capture the abrupt volatility changes typically present in impulsive noise, to improve artifact removal from ERPs. Two specifications are considered: (1) volatility driven by a heavy-tailed component and (2) transformation of volatility. Both result in volatility processes with heavy-tailed transition densities which can predict the impulsive noise volatility dynamics, more accurately than the Gaussian models. These SV noise models are incorporated in an autoregressive (AR) state-space ERP dynamic model. Parameter estimation is done using a Rao-Blackwellized particle filter (RBPF). Evaluation on simulated auditory brainstem responses (ABRs), corrupted by real eye-blink artifacts, shows that the non-Gaussian models can accurately detect the artifact-induced abrupt volatility spikes, and able to uncover the underlying inter-trial dynamics. Among them, the log-SV model performs the best. The results on real data demonstrate significant artifact suppression.

UTM-CIAM: Transformation and Beyond Malaysian Mathematics for Industry

This article deliberates on how the Malaysian industries and mathematicians have come to revive the synergy of mathematics and industry through the Malaysian Mathematics in Industry Study Groups (MISG 2011, 2014). The Malaysian setting of pre MISG was a disengaged connection between industries and mathematics. Post MISG 2011 and 2014 have seen intensified partnership between local industries and mathematical community beginning to crystallize. The founding of UTM Centre for Industrial and Applied Mathematics (UTM-CIAM) with seven permanent staff at the end 2012 was a follow-up effect of the MISG 2011. It is a positive transformation for the Malaysian Mathematics for Industry scene. The Malaysian MISG is organized in cooperation with Oxford Centre for Industrial and Applied Mathematics (OCIAM), University of Oxford. These are collaborative problem-solving workshops where more than seventy mathematicians, operational researchers and statisticians deal with real life problems brought up by six private and public companies. These workshops assist to find out promptly the key scientific issues and mathematical challenges to be confronted. The meeting provides opportunities for bridging the gap between academics and scientists from Malaysian industry, and encourages innovative knowledge and technology transfer. This work also summarizes the successful collaboration formed between academics and industry practitioners in solving specific problems from the national high revenue industries during the Malaysian MISG 2011 and 2014.

Deployment density estimation for α-Covering problem in wireless sensor network

Promising a suitable coverage is one of the problems in Wireless Sensor Network where a random deployment make it very difficult to measure. In this paper, a novel equation base on Gaussian distribution is proposed to estimate the deployment density. This function uses the α-Covering value and coverage percentage as inputs. Simulation results show high correlation between proposed equation and simulation data. Moreover, the average of the error in different scenarios is 0.38%.

Analysis of oil price fluctuations

Recently, crude oil price becomes volatile and have been the popular issue to be discussed in every country. Oil price fluctuations have major impact on the overall economy and finally will lead to increase in the inflation rate. It is important to describe these oil price fluctuations mathematically. This study aims to describe the above phenomena using geometric Brownian motion. Two crude oil prices, namely WTI and Brent have been analyzed based on daily oil price data from year 2000 until year 2015. Through the analysis using model assessment and model determination, crude oil price after year 2000 follows geometric Brownian motion process. We conclude that oil price fluctuations follow a geometric Brownian motion process without considering unexpected incidents.

Time delay and noise explaining the behaviour of the cell growth in fermentation process

This paper proposes to investigate the interplay between time delay and external noise in explaining the behaviour of the microbial growth in batch fermentation process. Time delay and noise are modelled jointly via stochastic delay differential equations (SDDEs). The typical behaviour of cell concentration in batch fermentation process under this model is investigated. Milstein scheme is applied for solving this model numerically. Simulation results illustrate the effects of time delay and external noise in explaining the lag and stationary phases, respectively for the cell growth of fermentation process.