Standard MATLAB Research Articles

Anti-Synchronization of Markovian Jumping Stochastic Chaotic Neural Networks with Mixed Time Delays

The anti-synchronization control is investigated for a class of uncertain stochastic chaotic neural networks with both Markovian jump parameters and mixed delays. The mixed delays consists of discrete and distributed time-varying delays. First, by combining the Lyapunov method and a generalized Halanay-type inequality for stochastic differential equations, a delay-dependent criterion is established to guarantee the state variables of the discussed stochastic chaotic neural networks to be globally exponential anti-synchronized. Next, by utilizing a novel lemma and the Jensen integral inequality, a delay-dependent criterion is proposed to achieve the globally stochastic robust anti-synchronization. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of linear matrix inequalities, which can be solved numerically by employing the standard Matlab LMI toolbox package. Finally, two examples are proposed to demonstrate the effectiveness and usefulness of the proposed results.

Robust stochastic convergence and stability of neutral‐type neural networks with Markovian jump and mixed delays

SummaryThe robust stochastic convergence and stability in mean square are investigated for a class of uncertain neutral‐type neural networks with both Markovian jump parameters and mixed delays. First, by employing the Lyapunov method and a generalized Halanay‐type inequality for stochastic differential equations, a delay‐dependent condition is derived to guarantee the state variables of the discussed neural networks to be globally uniformly exponentially stochastic convergent to a ball in the state space with a prespecified convergence rate. Next, by applying the Jensen integral inequality and a novel reciprocal convex lemma, a delay‐dependent criterion is developed to achieve the globally robust stochastic stability in mean square. With some parameters being fixed in advance, the proposed conditions are all expressed in terms of LMIs, which can be solved numerically by employing the standard MATLAB LMI toolbox package. Finally, two illustrated examples are given to show the effectiveness and less conservatism of the obtained results over some existing works. Copyright © 2014 John Wiley & Sons, Ltd.

Parallel Sequential Monte Carlo for Efficient Density Combination: The DeCo MATLAB Toolbox

This paper presents the Matlab package DeCo (Density Combination) which is based on the paper by Billio et al. (2013) where a constructive Bayesian approach is presented for combining predictive densities originating from different models or other sources of information. The combination weights are time-varying and may depend on past predictive forecasting performances and other learning mechanisms. The core algorithm is the function DeCo which applies banks of parallel Sequential Monte Carlo algorithms to filter the time-varying combination weights. The DeCo procedure has been implemented both for standard CPU computing and for Graphical Process Unit (GPU) parallel computing. For the GPU implementation we use the Matlab parallel computing toolbox and show how to use General Purposes GPU computing almost effortless. This GPU implementation comes with a speed up of the execution time up to seventy times compared to a standard CPU Matlab implementation on a multicore CPU. We show the use of the package and the computational gain of the GPU version, through some simulation experiments and empirical applications.

Fast algorithms for calculating the eigenvalues of normal Hankel matrices

Algorithms for the rapid computation of eigenvalues for certain classes of normal Toeplitz matrices are presented. The time required to execute these algorithms is compared to that of the standard Matlab procedure eig.

MATLAB-based program for optimization of quantum cascade laser active region parameters and calculation of output characteristics in magnetic field

A strong magnetic field applied along the growth direction of a quantum cascade laser (QCL) active region gives rise to a spectrum of discrete energy states, the Landau levels. By combining quantum engineering of a QCL with a static magnetic field, we can selectively inhibit/enhance non-radiative electron relaxation process between the relevant Landau levels of a triple quantum well and realize a tunable surface emitting device. An efficient numerical algorithm implementation is presented of optimization of GaAs/AlGaAs QCL region parameters and calculation of output properties in the magnetic field. Both theoretical analysis and MATLAB implementation are given for LO-phonon and interface roughness scattering mechanisms on the operation of QCL. At elevated temperatures, electrons in the relevant laser states absorb/emit more LO-phonons which results in reduction of the optical gain. The decrease in the optical gain is moderated by the occurrence of interface roughness scattering, which remains unchanged with increasing temperature. Using the calculated scattering rates as input data, rate equations can be solved and population inversion and the optical gain obtained. Incorporation of the interface roughness scattering mechanism into the model did not create new resonant peaks of the optical gain. However, it resulted in shifting the existing peaks positions and overall reduction of the optical gain. Program summaryProgram title: QCLCatalogue identifier: AERL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 37763No. of bytes in distributed program, including test data, etc.: 2757956Distribution format: tar.gzProgramming language: MATLAB.Computer: Any capable of running MATLAB version R2010a or higher.Operating system: Any platform supporting MATLAB version R2010a or higher.RAM: Minimum required is 1 GB. Memory usage increases for less intense magnetic fields.Classification: 15.Nature of problem:The nature of the problem is to provide an efficient numerical algorithm implementation for optimization of GaAs/AlGaAs QCL active region parameters and calculation of output properties in the magnetic field.Solution method:The optimization of the QCL laser performance at selected wavelength is performed at entire free-parameters space using simulated annealing algorithm. The scattering rates are calculated in the presence and without magnetic field and used as coefficients in rate equations. The standard MATLAB procedures were used to solve iteratively this system of equations and obtain distribution of electron densities over electronic states.Restrictions:The machine must provide the necessary main memory which decreases roughly quadratically with the increase of the magnetic field intensity.Running time:Optimization time on Intel 3 GHz processor is about 2×104 s. The calculation time of laser output properties for values set automatically in GUI is 5×104 s.

Erroneous cardiac ECG-gated PET list-mode trigger events can be retrospectively identified and replaced by an offline reprocessing approach: first results in rodents

The assessment of left ventricular function, wall motion and myocardial viability using electrocardiogram (ECG)-gated [18F]-FDG positron emission tomography (PET) is widely accepted in human and in preclinical small animal studies. The nonterminal and noninvasive approach permits repeated in vivo evaluations of the same animal, facilitating the assessment of temporal changes in disease or therapy response. Although well established, gated small animal PET studies can contain erroneous gating information, which may yield to blurred images and false estimation of functional parameters. In this work, we present quantitative and visual quality control (QC) methods to evaluate the accuracy of trigger events in PET list-mode and physiological data. Left ventricular functional analysis is performed to quantify the effect of gating errors on the end-systolic and end-diastolic volumes, and on the ejection fraction (EF). We aim to recover the cardiac functional parameters by the application of the commonly established heart rate filter approach using fixed ranges based on a standardized population. In addition, we propose a fully reprocessing approach which retrospectively replaces the gating information of the PET list-mode file with appropriate list-mode decoding and encoding software. The signal of a simultaneously acquired ECG is processed using standard MATLAB vector functions, which can be individually adapted to reliably detect the R-peaks. Finally, the new trigger events are inserted into the PET list-mode file. A population of 30 mice with various health statuses was analyzed and standard cardiac parameters such as mean heart rate (119 ms ± 11.8 ms) and mean heart rate variability (1.7 ms ± 3.4 ms) derived. These standard parameter ranges were taken into account in the QC methods to select a group of nine optimal gated and a group of eight sub-optimal gated [18F]-FDG PET scans of mice from our archive. From the list-mode files of the optimal gated group, we randomly deleted various fractions (5% to 60%) of contained trigger events to generate a corrupted group. The filter approach was capable to correct the corrupted group and yield functional parameters with no significant difference to the optimal gated group. We successfully demonstrated the potential of the fully reprocessing approach by applying it to the sub-optimal group, where the functional parameters were significantly improved after reprocessing (mean EF from 41% ± 16% to 60% ± 13%). When applied to the optimal gated group the fully reprocessing approach did not alter the functional parameters significantly (mean EF from 64% ± 8% to 64 ± 7%). This work presents methods to determine and quantify erroneous gating in small animal gated [18F]-FDG PET scans. We demonstrate the importance of a quality check for cardiac triggering contained in PET list-mode data and the benefit of optionally reprocessing the fully recorded physiological information to retrospectively modify or fully replace the cardiac triggering in PET list-mode data. We aim to provide a preliminary guideline of how to proceed in the presence of errors and demonstrate that offline reprocessing by filtering erroneous trigger events and retrospective gating by ECG processing is feasible. Future work will focus on the extension by additional QC methods, which may exploit the amplitude of trigger events and ECG signal by means of pattern recognition. Furthermore, we aim to transfer the proposed QC methods and the fully reprocessing approach to human myocardial PET/CT.

GPU accelerated greedy algorithms for compressed sensing

For appropriate matrix ensembles, greedy algorithms have proven to be an efficient means of solving the combinatorial optimization problem associated with compressed sensing. This paper describes an implementation for graphics processing units (GPU) of hard thresholding, iterative hard thresholding, normalized iterative hard thresholding, hard thresholding pursuit, and a two-stage thresholding algorithm based on compressive sampling matching pursuit and subspace pursuit. The GPU acceleration of the former bottleneck, namely the matrix–vector multiplications, transfers a significant portion of the computational burden to the identification of the support set. The software solves high-dimensional problems in fractions of a second which permits large-scale testing at dimensions currently unavailable in the literature. The GPU implementations exhibit up to 70\(\times \) acceleration over standard Matlab central processing unit implementations using automatic multi-threading.

Multi-machine power system state-space modelling for small-signal stability assessments

This work presents a general state-space representation of a multi-machine, multi-order power system model, which may be used to carry out small-signal stability assessments. Computational software coded in MATLAB has been developed in order to find and analyse the solution of an arbitrary number of synchronous generators in the network. Each generator is represented by a pre-defined model. The model choice is tailored to fit the available data for each generator. The software has provisions for conducting power flow solutions and the calculation of the initial state that the generators keep prior to the disturbance. The state-space representation and the equivalent transfer function matrix of the system are generated automatically. Eigenvalue analysis may be carried out using the standard MATLAB functionality. The paper is one of a tutorial nature and in order to check on the sanity of the results given by the new software, two text-book networks have been examined. The results were also compared with those generated using commercial industrial-grade software.

On grid generation with lemniscates of two and three foci

We construct orthogonal grids on meander-like regions, similar to riverbeds. The two boundaries of a meander-like region are fitted with segment pairs of lemniscates using standard nonlinear least squares MATLAB functions. We present as examples a long section of a river (composed of about sixty lemniscatic segments) and a flattened section of an aorta. The resulting grids are evaluated using standard grid quality parameters: the average aspect ratio, the maximum aspect ratio, and the average deviation from orthogonality and the maximum deviation from orthogonality.

New passivity conditions with fewer slack variables for uncertain neural networks with mixed delays

This paper introduces an effective approach to studying the passivity of neutral-type neural networks with discrete and continuous distributed time-varying delays. By employing a novel Lyapunov–Krasovskii functional based on delay partitioning, several improved delay-dependent passivity conditions are established to guarantee the passivity of uncertain neural networks by applying the Jensen integral inequality. These criteria are expressed in the framework of linear matrix inequalities, which can be verified easily by means of standard Matlab software. One special case of the obtained criteria turns out to be equivalent to some existing result with same reduced conservatism but including fewer slack variables. As the present passivity conditions involve fewer free-weighting matrices, the computational burden is largely reduced. Three examples are provided to demonstrate the advantage of the theoretical results.

Parallel Sequential Monte Carlo for Efficient Density Combination: The Deco Matlab Toolbox

This paper presents the Matlab package DeCo (Density Combination) which is based on the paper by Billio et al. (2013) where a constructive Bayesian approach is presented for combining predictive densities originating from different models or other sources of information. The combination weights are time-varying and may depend on past predictive forecasting performances and other learning mechanisms. The core algorithm is the function DeCo which applies banks of parallel Sequential Monte Carlo algorithms to filter the time-varying combination weights. The DeCo procedure has been implemented both for standard CPU computing and for Graphical Process Unit (GPU) parallel computing. For the GPU implementation we use the Matlab parallel computing toolbox and show how to use General Purposes GPU computing almost effortless. This GPU implementation comes with a speed up of the execution time up to seventy times compared to a standard CPU Matlab implementation on a multicore CPU. We show the use of the package and the computational gain of the GPU version, through some simulation experiments and empirical applications

Induced [formula omitted] norm control for LPV system with specified class of disturbance inputs

This paper presents a novel controller design approach for linear parameter-varying (LPV) systems to guarantee the stability with an induced L2 norm performance. Motivated by the idea of the generalized Kalman–Yakubovich–Popov (KYP) lemma, the spectral information of the disturbance inputs can be captured by a matrix-valued integral quadratic constraint. To a certain extent, this formulation not only weakens the function of weighting functions in the control synthesis but also reduces the order of the designed controller. The obtained controller design conditions for LPV systems are presented in terms of linear matrix inequalities (LMIs), which can be solved efficiently by the standard Matlab toolbox. The effectiveness of the proposed method is verified by solving a missile benchmark problem.

Robust exponential stability and H ∞ control for switched neutral‐type neural networks

SUMMARYIn this paper, we consider the problem of robust exponential stability for a class of uncertain switched delayed neutral‐type neural networks with an H ∞ performance level γ > 0. Further, the result is extended to design an H ∞ control law to ensure the robust exponential stabilization of the closed‐loop neural networks about its equilibrium point with the guaranteed H ∞ performance level γ, for all norm bounded parameter uncertainties. On the basis of a new set of Lyapunov–Krasovskii functional, linear matrix inequality technique, and average dwell time approach, a set of novel sufficient conditions is derived for the existence of H ∞ performance and as well as existence of H ∞ control problem. The obtained results are derived in the form of convex optimization problems, which can be solved easily by the standard Matlab control toolbox. Numerical examples with simulation results are provided to illustrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Improvement of Power Factor and Harmonic Elimination in Distribution Line using PI with Hysteresis Current Controller

Power quality improvement is a major research area in current context. Though much work has been done by many researchers still scope is there to work on this area. In this paper an attempt is made to eliminate the harmonics as well as for the improvement of power factor. Here distribution static synchronous compensator (DSTATCOM) is used to improve power factor in distribution line & mitigate harmonics with an optional feature of voltage regulation. Further the frequency analysis of the distribution line is analyzed both before & after compensation. A relay based hysteresis current regulator is used for DSTATCOM controller in indirect current control technique. Simulation is carried out in standard MATLAB environment. Results of simulations are presented for linear & nonlinear load.

Object-oriented CRONE toolbox for fractional differential signal processing

The CRONE toolbox, developed since the nineties by the CRONE team, is a Matlab toolbox dedicated to fractional calculus and its applications in signal processing and automatic control. It is currently evolving toward an object-oriented version, which allows many enhancements. Three main classes, dedicated to fractional system representations namely fractional transfer functions (frac_tf), fractional zeros poles and gain (frac_zpk), and fractional state-space (frac_ss), are developed. All three user classes are children of a parent class (frac_lti) that contains some common attributes of fractional systems. Among the enhancements of the object programming of the CRONE toolbox is the overloading of basic operators (+, −, ×, /, .×, …) and standard Matlab scripts (lsim, bode, nichols, …) for the new classes. As a consequence, an end-user familiar with standard Matlab operators and scripts can use straightforwardly the CRONE toolbox. The main objective of this paper is to present class diagrams and principle features of the object-oriented CRONE toolbox, which can be downloaded at http://cronetoolbox.ims-bordeaux.fr.

On a Closed Form for the Noncoherent Gain Factor

Instead of using the empirical algebraic expression offered by H. Urkowitz for noncoherent gain factor calculations, standard MATLAB commands may be successfully applied.

Towards an object oriented CRONE Toolbox for fractional differential systems

AbstractThe CRONE Toolbox, developed since the nineties by the CRONE team, is a Matlab Toolbox dedicated to fractional calculus. It is currently evolving towards an object oriented version, which allows many enhancements. Three main user classes, dedicated to fractional systems representations namely fractional transfer functions (frac_tf), fractional zeros poles and gain (frac_zpk), and fractional state-space (frac_ss), are developed. All three user classes are children of a parent class (frac_lti) which contains some common attributes of fractional systems. Among enhancements of the object programming of the CRONE toolbox, is the overloading of basic operators (+, –, x, /, .x, …) and standard Matlab scripts (lsim, bode, nichols, …) for the new classes. As a consequence, an end user familiar with standard Matlab operators and scripts can use straightforwardly the CRONE toolbox. The main objective of this paper is to present class diagrams and principle features of the object oriented CRONE toolbox, which can be downloaded at http://cronetoolbox.ims-bordeaux.frcronetoolbox.ims-bordeaux.fr.

Application of Scale Relativity (ScR) Theory to the Problem of a Particle in a Finite One-Dimensional Square Well (FODSW) Potential

In the present work, and along the lines of Hermann, ScR theory is applied to a finite one-dimensional square well potential problem. The aim is to show that scale relativity theory can reproduce quantum mechanical results without employing the Schrödinger equation. Some mathematical difficulties that arise when obtaining the solution to this problem were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potential utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within limited local computer facilities [1,2]. Comparison of the present results with the corresponding results obtained from conventional quantum mechanics by solving the Schrödinger equation, shows very good agreement. This agreement was improved further by optimizing the parameters used in the numerical simulations [1,3]. This represents a new example where scale relativity theory, based on a fractal space-time concept, can accurately reproduce quantum mechanical results without invoking the Schrödinger equation.

A neural network approach for the prediction of in vitro culture parameters for maximum biomass yields in hairy root cultures

The present study deals with ANN based prediction of culture parameters in terms of inoculum density, pH and volume of growth medium per culture vessel and sucrose content of the growth medium for Glycyrrhiza hairy root cultures. This kind of study could be a model system in exploitation of hairy root cultures for commercial production of pharmaceutical compounds using large bioreactors. The study is aimed to evaluate the efficiency of regression neural network and back propagation neural network for the prediction of optimal culture conditions for maximum hairy root biomass yield. The training data for regression and back propagation networks were primed on the basis of function approximation, where final biomass fresh weight ( f wt ) was considered as a function of culture parameters. On this basis the variables in culture conditions were described in the form of equations which are for inoculum density: y=0.02 x+0.04, for pH of growth medium: y= x+2.8, for sucrose content in medium: y=9.9464 x+(−9.7143) and for culture medium per culture vessel: y=10 x. The fresh weight values obtained from training data were considered as target values and further compared with predicted fresh weight values. The empirical data were used as testing data and further compared with values predicted from trained networks. Standard MATLAB inbuilt generalized regression network with radial basis function radbas as transfer function in layer one and purelin in layer two and back propagation having purelin as transfer function in output layer and logsig in hidden layer were used. Although in comparative assessment both the networks were found efficient for prediction of optimal culture conditions for high biomass production, more accuracy in results was seen with regression network.

Numerical experiments with algorithms for the ADI and Zolotarev coefficients

In this paper, we present numerical experiments comparing the algorithms for computing the ADI and Zolotarev coefficients which involve Jacobi elliptic functions and the complete elliptic integral. We show that in some cases the algorithms, which use the standard MATLAB functions for computing the Jacobi elliptic functions and the complete elliptic integral, are less accurate than the algorithm of Zie¸tak, which can be applied when the number of coefficients is a power of 2. The algorithm of Zie¸tak is also competitive with the algorithms of Wachspress and Kennedy.