An optimisation of Gaussian mixture models for integer processing units

This paper investigates sub-integer implementations of the adaptive Gaussian mixture model (GMM) for background/foreground segmentation to allow the deployment of the method on low cost/low power processors that lack Floating Point Unit (FPU). We propose two novel integer computer arithmetic techniques to update Gaussian parameters. Specifically, the mean value and the variance of each Gaussian are updated by a redefined and generalised "round'' operation that emulates the original updating rules for a large set of learning rates. Weights are represented by counters that are updated following stochastic rules to allow a wider range of learning rates and the weight trend is approximated by a line or a staircase. We demonstrate that the memory footprint and computational cost of GMM are significantly reduced, without significantly affecting the performance of background/foreground segmentation.

Effect of magnetic bias on Gaussian pulse scattering by stacked nonlinear semiconductor layers

The nonlinear scattering of pulses by periodic stacks of semiconductor layers with magnetic bias has been studied in the self-consistent problem formulation, taking into account mobility of carriers. The three-wave mixing technique has been applied to the analysis of the waveform evolution in the stacks illuminated by two Gaussian pulses with different central frequencies and lengths. The effects of external magnetic bias, and stack physical and geometrical parameters on the properties of the scattered waveforms are discussed. © 2013 IEEE.

Gaussian States in Quantum Information

These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.

A dynamic sampling methodology for plasma etch processes using Gaussian process regression

Plasma etch is a key process in modern semiconductor manufacturing facilities as it offers process simplification and yet greater dimensional tolerances compared to wet chemical etch technology. The main challenge of operating plasma etchers is to maintain a consistent etch rate spatially and temporally for a given wafer and for successive wafers processed in the same etch tool. Etch rate measurements require expensive metrology steps and therefore in general only limited sampling is performed. Furthermore, the results of measurements are not accessible in real-time, limiting the options for run-to-run control. This paper investigates a Virtual Metrology (VM) enabled Dynamic Sampling (DS) methodology as an alternative paradigm for balancing the need to reduce costly metrology with the need to measure more frequently and in a timely fashion to enable wafer-to-wafer control. Using a Gaussian Process Regression (GPR) VM model for etch rate estimation of a plasma etch process, the proposed dynamic sampling methodology is demonstrated and evaluated for a number of different predictive dynamic sampling rules. © 2013 IEEE.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

Gaussian pulse mixing by stacked semiconductor layers

The nonlinear scattering of two Gaussian pulses with different central frequencies incident at slant angles on the periodic stack of binary semiconductor layers has been modelled in the self-consistent problem formulation taking into account the dynamics of charges. The effects of the pump pulse length and central frequencies, and the stack physical and geometrical parameters on the properties of the emitted combinatorial frequency waveforms are analysed and discussed.

Hybrid probabilistic wind power forecasting using temporally local Gaussian process

The demand for sustainable development has resulted in a rapid growth in wind power worldwide. Despite various approaches have been proposed to improve the accuracy and to overcome the uncertainties associated with traditional methods, the stochastic and variable nature of wind still remains the most challenging issue in accurately forecasting wind power. This paper presents a hybrid deterministic-probabilistic method where a temporally local ‘moving window’ technique is used in Gaussian Process to examine estimated forecasting errors. This temporally local Gaussian Process employs less measurement data while faster and better predicts wind power at two wind farms, one in the USA and the other in Ireland. Statistical analysis on the results shows that the method can substantially reduce the forecasting error while more likely generate Gaussian-distributed residuals, particularly for short-term forecast horizons due to its capability to handle the time-varying characteristics of wind power.

Special condition wind power forecasting based on Gaussian process and similar historical data

Due to the variability of wind power, it is imperative to accurately and timely forecast the wind generation to enhance the flexibility and reliability of the operation and control of real-time power. Special events such as ramps, spikes are hard to predict with traditional methods using solely recently measured data. In this paper, a new Gaussian Process model with hybrid training data taken from both the local time and historic dataset is proposed and applied to make short-term predictions from 10 minutes to one hour ahead. A key idea is that the similar pattern data in history are properly selected and embedded in Gaussian Process model to make predictions. The results of the proposed algorithms are compared to those of standard Gaussian Process model and the persistence model. It is shown that the proposed method not only reduces magnitude error but also phase error.

Performance assessment of cascade control loopswith non-Gaussian disturbances using entropy information

Cascade control is one of the routinely used control strategies in industrial processes because it can dramatically improve the performance of single-loop control, reducing both the maximum deviation and the integral error of the disturbance response. Currently, many control performance assessment methods of cascade control loops are developed based on the assumption that all the disturbances are subject to Gaussian distribution. However, in the practical condition, several disturbance sources occur in the manipulated variable or the upstream exhibits nonlinear behaviors. In this paper, a general and effective index of the performance assessment of the cascade control system subjected to the unknown disturbance distribution is proposed. Like the minimum variance control (MVC) design, the output variances of the primary and the secondary loops are decomposed into a cascade-invariant and a cascade-dependent term, but the estimated ARMA model for the cascade control loop based on the minimum entropy, instead of the minimum mean squares error, is developed for non-Gaussian disturbances. Unlike the MVC index, an innovative control performance index is given based on the information theory and the minimum entropy criterion. The index is informative and in agreement with the expected control knowledge. To elucidate wide applicability and effectiveness of the minimum entropy cascade control index, a simulation problem and a cascade control case of an oil refinery are applied. The comparison with MVC based cascade control is also included.

Time series wind power forecasting based on variant Gaussian process and TLBO

Due to the variability and stochastic nature of wind power system, accurate wind power forecasting has an important role in developing reliable and economic power system operation and control strategies. As wind variability is stochastic, Gaussian Process regression has recently been introduced to capture the randomness of wind energy. However, the disadvantages of Gaussian Process regression include its computation complexity and incapability to adapt to time varying time-series systems. A variant Gaussian Process for time series forecasting is introduced in this study to address these issues. This new method is shown to be capable of reducing computational complexity and increasing prediction accuracy. It is further proved that the forecasting result converges as the number of available data approaches innite. Further, a teaching learning based optimization (TLBO) method is used to train the model and to accelerate
the learning rate. The proposed modelling and optimization method is applied to forecast both the wind power generation of Ireland and that from a single wind farm to show the eectiveness of the proposed method.