Dynamics of dark hollow Gaussian laser pulses in relativistic plasma

Optical beams with null central intensity have potential applications in the field of atom optics. The spatial and temporal evolution of a central shadow dark hollow Gaussian (DHG) relativistic laser pulse propagating in a plasma is studied in this article for first principles. A nonlinear Schrodinger-type equation is obtained for the beam spot profile and then solved numerically to investigate the pulse propagation characteristics. As series of numerical simulations are employed to trace the profile of the focused and compressed DHG laser pulse as it propagates through the plasma. The theoretical and simulation results predict that higher-order DHG pulses show smaller divergence as they propagate and, thus, lead to enhanced energy transport. © 2013 American Physical Society.

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.

Taguchi optimisation approach for production of activated carbon from phosphoric acid impregnated palm kernel shell by microwave heating

Taguchi method was applied to investigate the optimal operating conditions in the preparation of activated carbon using palm kernel shell with quadruple control factors: irradiation time, microwave power, concentration of phosphoric acid as impregnation substance and impregnation ratio between acid and palm kernel shell. The best combination of the control factors as obtained by applying Taguchi method was microwave power of 800 W, irradiation time of 17 min, impregnation ratio of 2, and acid concentration of 85%. The noise factor (particle size of raw material) was considered in a separate outer array, which had no effect on the quality of the activated carbon as confirmed by t-test. Activated carbon prepared at optimum combination of control factors had high BET surface area of 1,473.55 m² g-1 and high porosity. The adsorption equilibrium and kinetic data can satisfactorily be described by the Langmuir isotherm and a pseudo-second-order kinetic model, respectively. The maximum adsorbing capacity suggested by the Langmuir model was 1000 mg g-1.

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.

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.

Kernel-based local order estimation of nonlinear nonparametric systems

We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples.

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.

Kernel based approaches to local nonlinear non-parametric variable selection

In this paper, we consider the variable selection problem for a nonlinear non-parametric system. Two approaches are proposed, one top-down approach and one bottom-up approach. The top-down algorithm selects a variable by detecting if the corresponding partial derivative is zero or not at the point of interest. The algorithm is shown to have not only the parameter but also the set convergence. This is critical because the variable selection problem is binary, a variable is either selected or not selected. The bottom-up approach is based on the forward/backward stepwise selection which is designed to work if the data length is limited. Both approaches determine the most important variables locally and allow the unknown non-parametric nonlinear system to have different local dimensions at different points of interest. Further, two potential applications along with numerical simulations are provided to illustrate the usefulness of the proposed algorithms.