Search results for: stationary Gaussian processes

Authors: Kai Chen, Shuguang Cui, Feng Yin

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Gaussian process (GP) with spectral mixture (SM) kernel demonstrates flexible non-parametric Bayesian learning ability in modeling unknown function. In this work a novel time-varying and non-stationary convolution spectral mixture (TN-CSM) kernel with a significant enhancing of interpretability by using process convolution is introduced. A way decomposing the SM component into an auto-convolution of base SM component and parameterizing it to be input dependent is outlined. Smoothly, performing a convolution between two base SM component yields a novel structure of non-stationary SM component with much better generalized expression and interpretation. The TN-CSM perfectly allows compatibility with the stationary SM kernel in terms of kernel form and spectral base ignored and confused by previous non-stationary kernels. On synthetic and real-world datatsets, experiments show the time-varying characteristics of hyper-parameters in TN-CSM and compare the learning performance of TN-CSM with popular and representative non-stationary GP.

Keywords: Gaussian process, spectral mixture, non-stationary, convolution

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: S. Benkraouda, Z. Djelloul-Khedda, B. Yagoubi

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we present a method for early detection of forest fires from a thermal infrared satellite image, using the image matrix of the probability of belonging. The principle of the method is to compare a theoretical mathematical model to an experimental model. We considered that each line of the image matrix, as an embodiment of a non-stationary random process. Since the distribution of pixels in the satellite image is statistically dependent, we divided these lines into small stationary and ergodic intervals to characterize the image by an adequate mathematical model. A standard deviation was chosen to generate random variables, so each interval behaves naturally like white Gaussian noise. The latter has been selected as the mathematical model that represents a set of very majority pixels, which we can be considered as the image background. Before modeling the image, we made a few pretreatments, then the parameters of the theoretical Gaussian model were extracted from the modeled image, these settings will be used to calculate the probability of each interval of the modeled image to belong to the theoretical Gaussian model. The high intensities pixels are regarded as foreign elements to it, so they will have a low probability, and the pixels that belong to the background image will have a high probability. Finally, we did present the reverse of the matrix of probabilities of these intervals for a better fire detection.

Keywords: forest fire, forest fire detection, satellite image, normal distribution, theoretical gaussian model, thermal infrared matrix image

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Authors: Jane A. Luke

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Persistent pressure passed on to manufacturers from escalating consumer expectations and the ever growing global competitiveness have produced a rapidly increasing interest in the development of various manufacturing strategy models. Academic and industrial circles are taking keen interest in the field of manufacturing strategy. Many manufacturing strategies are currently centered on the traditional concepts of focused manufacturing capabilities such as quality, cost, dependability and innovation. Process capability indices was conducted assuming that the process under study is in statistical control and independent observations are generated over time. However, in practice, it is very common to come across processes which, due to their inherent natures, generate autocorrelated observations. The degree of autocorrelation affects the behavior of patterns on control charts. Even, small levels of autocorrelation between successive observations can have considerable effects on the statistical properties of conventional control charts. When observations are autocorrelated the classical control charts exhibit nonrandom patterns and lack of control. Many authors have considered the effect of autocorrelation on the performance of statistical process control charts. In this paper, the effect of autocorrelation on confidence intervals for different PCIs was included. Stationary Gaussian processes is explained. Effect of autocorrelation on PCIs is described in detail. Confidence intervals for Cp and Cpk are constructed for PCIs when data are both independent and autocorrelated. Confidence intervals for Cp and Cpk are computed. Approximate lower confidence limits for various Cpk are computed assuming AR(1) model for the data. Simulation studies and industrial examples are considered to demonstrate the results.

Keywords: autocorrelation, AR(1) model, Bissell’s approximation, confidence intervals, statistical process control, specification limits, stationary Gaussian processes

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Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui

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The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: wind power, Gaussien process, modelling, forecasting

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Authors: Andrew Clark

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McCauley, Bassler, and Gunaratne show that integration I(d) processes as used in economics and finance do not necessarily produce stationary increments, which are required to determine causality in both the short term and the long term. This paper follows their lead and shows I(d) aluminum cash and futures log prices at daily and weekly intervals do not have stationary increments, which means prior causality studies using I(d) processes need to be re-examined. Wavelets based on undifferenced cash and futures log prices do have stationary increments and are used along with transfer entropy (versus cointegration) to measure causality. Wavelets exhibit causality at most daily time scales out to 1 year, and weekly time scales out to 1 year and more. To determine stationarity, localized stationary wavelets are used. LSWs have the benefit, versus other means of testing for stationarity, of using multiple hypothesis tests to determine stationarity. As informational flows exist between cash and futures at daily and weekly intervals, the aluminum market is efficient. Therefore, hedges used by producers and consumers of aluminum need not have a big concern in terms of the underestimation of hedge ratios. Questions about arbitrage given efficiency are addressed in the paper.

Keywords: transfer entropy, nonstationary increments, wavelets, localized stationary wavelets, localized stationary wavelets

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Authors: Mounir Zili

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We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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Authors: Mounir Zili

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We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Katsumi Hirata

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To develop the useful acoustic environmental recognition system, the method of estimating 3D-position of a stationary random acoustic source using bispectral analysis of 4-point detected signals is proposed. The method uses information about amplitude attenuation and propagation delay extracted from amplitude ratios and angles of auto- and cross-bispectra of the detected signals. It is expected that using bispectral analysis affects less influence of Gaussian noises than using conventional power spectral one. In this paper, the basic principle of the method is mentioned first, and its validity and features are considered from results of the fundamental experiments assumed ideal circumstances.

Keywords: 4-point detection, a stationary random acoustic source, auto- and cross-bispectra, estimation of 3D-position

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Samaneh Rahimirshnani, Hossein Jafari

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In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: A. Keshavarz

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A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: beam propagation, cos-Gaussian beam, numerical simulation, photorefractive crystal

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Authors: Keunhong Chae, Seokho Yoon

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In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol

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Authors: Loïc Warscotte, Jehan Boreux

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The scientific literature of changepoint detection is vast. Today, a lot of methods are available to detect abrupt changes or slight drift in a signal, based on CUSUM or EWMA charts, for example. However, these methods rely on strong assumptions, such as the stationarity of the stochastic underlying process, or even the independence and Gaussian distributed noise at each time. Recently, the breakthrough research on locally stationary processes widens the class of studied stochastic processes with almost no assumptions on the signals and the nature of the changepoint. Despite the accurate description of the mathematical aspects, this methodology quickly suffers from impractical time and space complexity concerning the signals with high-rate data collection, if the characteristics of the process are completely unknown. In this paper, we then addressed the problem of making this theory usable to our purpose, which is monitoring a high-speed weigh-in-motion system (HS-WIM) towards direct enforcement without supervision. To this end, we first compute bounded approximations of the initial detection theory. Secondly, these approximating bounds are empirically validated by generating many independent long-run stochastic processes. The abrupt changes and the drift are both tested. Finally, this relaxed methodology is tested on real signals coming from a HS-WIM device in Belgium, collected over several months.

Keywords: changepoint, weigh-in-motion, process, non-parametric

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Authors: Bruna G. M. Araújo, Pedro M. M. Q. Cruz

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In this letter, we review the literature of the major concepts that govern Gaussian quantum information. As we work with quantum information and computation with continuous variables, Gaussian states are needed to better describe these systems. Analyzing a single ion locked in a Paul trap we use the interaction picture to obtain a toolbox of Gaussian operations with the ion-laser interaction Hamiltionian. This is achieved exciting the ion through the combination of two lasers of distinct frequencies corresponding to different sidebands of the external degrees of freedom. First we study the case of a trap with 1 mode and then the case with 2 modes. In this way, we achieve different continuous variables gates just by changing the external degrees of freedom of the trap and combining the Hamiltonians of blue and red sidebands.

Keywords: Paul trap, ion-laser interaction, Gaussian operations

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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Authors: Vinci Mojamdar, Govind S. Gupta

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Moving beds in the presence of gas flow are widely used in metallurgical and chemical industries like blast furnaces, catalyst reforming, drying, etc. Pressure drop studies in co- and counter – current conditions have been done by a few researchers. However, to the best of authours knowledge, proper pressure drop study with lateral gas injection lacks especially in the presence of cavity and nozzle protrusion inside the packed bed. The latter study is more useful for metallurgical industries for the processes such as blast furnaces, shaft reduction and, COREX. In this experimental work, a two dimensional cold model with slot type nozzle for lateral gas injection along with the plastic beads as packing material and dry air as gas have been used. The variation of pressure drop is recorded at various horizontal and vertical directions in the presence of cavity and nozzle protrusion. The study has been performed in both moving and stationary beds. Also, the experiments have been carried out in both increasing as well as decreasing gas flow conditions. Experiments have been performed at various gas flow rates and packed bed heights. Some interesting results have been reported such as there is no pressure variation in the moving bed for both the increasing and decreasing gas flow condition that is different from the stationary bed. Pressure hysteresis loop has been observed in a stationary bed.

Keywords: lateral gas injection, moving bed, pressure drop, pressure hysteresis, stationary bed

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

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Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: artificial immune system, breast cancer diagnosis, Euclidean function, Gaussian function

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Authors: Anand Prakash Dwivedi, Sounak Kumar Choudhury

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Electric Discharge Machining (EDM) is a well-established and one of the most primitive unconventional manufacturing processes, that is used world-wide for the machining of geometrically complex or hard and electrically conductive materials which are extremely difficult to cut by any other conventional machining process. One of the major flaws, over all its advantages, is its very slow Material Removal Rate (MRR). In order to eradicate this slow machining rate, various researchers have proposed various methods like; providing rotational motion to the tool or work-piece or to both, mixing of conducting additives (such as SiC, Cr, Al, graphite etc) powders in the dielectric, providing vibrations to the tool or work-piece or to both etc. Present work is a comparative study of Rotational and Stationary Tool EDM, which deals with providing rotational motion to the copper tool for the machining of AISI D3 Tool Steel and the results have been compared with stationary tool EDM. It has been found that the tool rotation substantially increases the MRR up to 28%. The average surface finish increases around 9-10% by using the rotational tool EDM. The average tool wear increment is observed to be around 19% due to the tool rotation. Apart from this, the present work also focusses on the recast layer analysis, which are being re-deposited on the work-piece surface during the operation. The recast layer thickness is less in case of Rotational EDM and more for Stationary Tool EDM. Moreover, the cracking on the re-casted surface is also more for stationary tool EDM as compared with the rotational EDM.

Keywords: EDM, MRR, Ra, TWR

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Swathi Gopakumar, Sruthi Krishna, Shivasubramani Krishnamoorthy

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Contactless, painless and radiation-free thermal imaging technology is one of the preferred screening modalities for detection of breast cancer. However, poor signal to noise ratio and the inexorable need to preserve edges defining cancer cells and normal cells, make the segmentation process difficult and hence unsuitable for computer-aided diagnosis of breast cancer. This paper presents key findings from a research conducted on the appraisal of two promising techniques, for the detection of breast cancer: (I) marker-controlled, Level-set segmentation of anisotropic diffusion filtered preprocessed image versus (II) Segmentation using marker-controlled level-set on a Gaussian-filtered image. Gaussian-filtering processes the image uniformly, whereas anisotropic filtering processes only in specific areas of a thermographic image. The pre-processed (Gaussian-filtered and anisotropic-filtered) images of breast samples were then applied for segmentation. The segmentation of breast starts with initial level-set function. In this study, marker refers to the position of the image to which initial level-set function is applied. The markers are generally placed on the left and right side of the breast, which may vary with the breast size. The proposed method was carried out on images from an online database with samples collected from women of varying breast characteristics. It was observed that the breast was able to be segmented out from the background by adjustment of the markers. From the results, it was observed that as a pre-processing technique, anisotropic filtering with level-set segmentation, preserved the edges more effectively than Gaussian filtering. Segmented image, by application of anisotropic filtering was found to be more suitable for feature extraction, enabling automated computer-aided diagnosis of breast cancer.

Keywords: anisotropic diffusion, breast, Gaussian, level-set, thermograms

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Authors: Sandeep Kumar, Naveen Gupta

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The propagation of the Non-Gaussian laser beam results in strong self-focusing as compare to the Gaussian laser beam, which helps to achieve a prerequisite of the plasma-based electron, Terahertz generation, and higher harmonic generations. The theoretical investigation on the evolution of non-Gaussian laser beam through the collisional plasma with ramped density has been presented. The non-uniform irradiance over the cross-section of the laser beam results in redistribution of the carriers that modifies the optical response of the plasma in such a way that the plasma behaves like a converging lens to the laser beam. The formulation is based on finding a semi-analytical solution of the nonlinear Schrodinger wave equation (NLSE) with the help of variational theory. It has been observed that the decentred parameter ‘q’ of laser and wavenumber of ripples of medium contribute to providing the required conditions for the improvement of self-focusing.

Keywords: non-Gaussian beam, collisional plasma, variational theory, self-focusing

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Authors: M. Yoneda

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It is known that stationary human occupants act as dynamic mass-spring-damper systems and can change the modal properties of civil engineering structures. This paper describes the full scale measurement to explain the tuned mass damper effects of stationary people on structural damping of footbridge with center span length of 33 m. A human body can be represented by a lumped system consisting of masses, springs, and dashpots. Complex eigenvalue calculation is also conducted by using ISO5982:1981 human model (two degree of freedom system). Based on experimental and analytical results for the footbridge with the stationary people in the standing position, it is demonstrated that stationary people behave as a tuned mass damper and that ISO5982:1981 human model can explain the structural damping characteristics measured in the field.

Keywords: dynamic interaction, footbridge, stationary people, structural damping

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Authors: Yasser Aldali

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The scope of this paper is to evaluate and compare the potential of LS-PV (Large Scale Photovoltaic Power Plant) power generation systems in the southern region of Libya at Al-Kufra for both stationary and tracking systems. A Microsoft Excel-VBA program has been developed to compute slope radiation, dew-point, sky temperature, and then cell temperature, maximum power output and module efficiency of the system for stationary system and for tracking system. The results for energy production show that the total energy output is 114GWh/year for stationary system and 148 GWh/year for tracking system. The average module efficiency for the stationary system is 16.6% and 16.2% for the tracking system. The values of electricity generation capacity factor (CF) and solar capacity factor (SCF) for stationary system were found to be 26% and 62.5% respectively and 34% and 82% for tracking system. The GCR (Ground Cover Ratio) for a stationary system is 0.7, which corresponds to a tilt angle of 24°. The GCR for tracking system was found to be 0.12. The estimated ground area needed to build a 50MW PV plant amounts to approx. 0.55 km2 for a stationary PV field constituted by HIT PV arrays and approx. 91 MW/km2. In case of a tracker PV field, the required ground area amounts approx. 2.4k m2 and approx. 20.5 MW/km2.

Keywords: large scale photovoltaic power plant, two-axis tracking system, stationary system, landscape impact

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Authors: Lina Pan

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In non-Gaussian clutter of a spherically invariant random vector, in the cases that a certain estimated covariance matrix could become singular, the adaptive target detection of high-range-resolution radar is addressed. Firstly, the restricted maximum likelihood (RML) estimates of unknown covariance matrix and scatterer amplitudes are derived for non-Gaussian clutter. And then the RML estimate of texture is obtained. Finally, a novel detector is devised. It is showed that, without secondary data, the proposed detector outperforms the existing Kelly binary integrator.

Keywords: non-Gaussian clutter, covariance matrix estimation, target detection, maximum likelihood

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Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri

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In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, gaussian mixture models, learning motion patterns, tracked robots for urban search and rescue

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: M. T. Alodat

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In this paper, we propose a generalization to the Gaussian process regression(GPR) model called the extended skew Gaussian process for regression(ESGPr) model. The ESGPR model works better than the GPR model when the errors are skewed. We derive the predictive distribution for the ESGPR model at a new input. Also we apply the ESGPR model to FOREX data and we find that it fits the Forex data better than the GPR model.

Keywords: extended skew normal distribution, Gaussian process for regression, predictive distribution, ESGPr model

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Authors: Abhisek Sinha, Debobrata Rajak, Shilpa Rani, Ram Gopal, Vandana Sharma

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The interaction of femtosecond laser pulses with metallic tips has been studied extensively, and they have proved to be a very good source of ultrashort electron pulses. A study of the interaction of femtosecond Laguerre-Gaussian (LG) laser modes with Tungsten tips is presented here. Laser pulses of 35 fs pulse durations were incident on Tungsten tips, and their electron emission rates were studied for LG (l=1, p=0) and Gaussian modes. A change in the order of the interaction for LG beams is reported, and the difference in the order of interaction is attributed to ponderomotive shifts in the energy levels corresponding to the enhanced near-field intensity supported by numerical simulations.

Keywords: femtosecond, Laguerre-Gaussian, OAM, tip

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