Search results for: stochastic approximation gradient

Authors: Najrullah Khan, Athar Ali Khan

Abstract:

The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

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Authors: Zaid Jamal Saeed Almahmoud

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Smart grid is emerging as the future power grid, with smart techniques to optimize power consumption and electricity generation. Minimizing peak power consumption under a fixed delay requirement is a significant problem in the smart grid.For this problem, all appliances must be scheduled within a given finite time duration. We consider the problem of minimizing the peak demand under appliances constraints by scheduling power jobs with uniform release dates and deadlines. As the problem is known to be NP-hard, we analyze the performance of a version of the natural greedy heuristic for solving this problem. Our theoretical analysis and experimental results show that the proposed heuristic outperforms existing methods by providing a better approximation to the optimal solution.

Keywords: peak demand scheduling, approximation algorithms, smart grid, heuristics

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Authors: Tomoaki Hashimoto

Abstract:

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

Procedia PDF Downloads 422

Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad, T. Lantri, A. Zitouni

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The purpose of this study was to investigate the structural,electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3. It includes our calculations based on the use of the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, The spin polarized electronic band structures and densities of states as well as the integer value of the magnetic moment of the unit cell (6 μB) illustrate that PrMnO3 is half-metallic ferromagnetic. The study prove that the compound is half-metallic ferromagnetic however the results obtained, make the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: cubic, DFT, electronic properties, magnetic moment, spintronics

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Authors: G. Patricia Abdel Rahim, Jairo Arbey Rodriguez M, María Guadalupe Moreno Armenta

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The present study shows the structural, electronic and magnetic properties of magnesium (Mg) and bismuth (Bi) in a supercell (1X1X5). For both materials were studied in five crystalline structures: rock salt (NaCl), cesium chloride (CsCl), zinc-blende (ZB), wurtzite (WZ), and nickel arsenide (NiAs), using the Density Functional Theory (DFT), the Generalized Gradient Approximation (GGA), and the Full Potential Linear Augmented Plane Wave (FP-LAPW) method. By means of fitting the Murnaghan's state equation we determine the lattice constant, the bulk modulus and it's derived with the pressure. Also we calculated the density of states (DOS) and the band structure.

Keywords: bismuth, magnesium, pseudo-potential, supercell

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Authors: Armin Rahimi

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In this study, we reveal co-seismic signals of two combined earthquakes, the 2006 Mw8.3 thrust and 2007 Mw8.1 normal fault earthquakes of the central Kuril Islands from GRACE observations. We compute monthly full gravitational gradient tensor in the local north-east-down frame for Kuril Islands earthquakes without spatial averaging and de-striping filters. Some of the gravitational gradient components (e.g. ΔVxx, ΔVxz) enhance high frequency components of the earth gravity field and reveal more details in spatial and temporal domain. Therefore that preseismic activity can be better illustrated. We show that the positive-negative-positive co-seismic ΔVxx due to the Kuril Islands earthquakes ranges from − 0.13 to + 0.11 milli Eötvös, and ΔVxz shows a positive-negative-positive pattern ranges from − 0.16 to + 0.13 milli Eötvös, agree well with seismic model predictions.

Keywords: GRACE observation, gravitational gradient changes, Kuril island earthquakes, PSGRN/PSCMP

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: area-based traffic, car-following model, micro-simulation, stochastic modeling

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Authors: Bingxi Huang, Yiqing Li, Marek Morzynski, Bernd R. Noack

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We propose a Kriging-based global optimization method for active flow control with multiple actuation parameters. This method is designed to converge quickly and avoid getting trapped into local minima. We follow the model-free explorative gradient method (EGM) to alternate between explorative and exploitive steps. This facilitates a convergence similar to a gradient-based method and the parallel exploration of potentially better minima. In contrast to EGM, both kinds of steps are performed with Kriging surrogate model from the available data. The explorative step maximizes the expected improvement, i.e., favors regions of large uncertainty. The exploitive step identifies the best location of the cost function from the Kriging surrogate model for a subsequent weight-biased linear-gradient descent search method. To verify the effectiveness and robustness of the improved Kriging-based optimization method, we have examined several comparative test problems of varying dimensions with limited evaluation budgets. The results show that the proposed algorithm significantly outperforms some model-free optimization algorithms like genetic algorithm and differential evolution algorithm with a quicker convergence for a given budget. We have also performed direct numerical simulations of the fluidic pinball (N. Deng et al. 2020 J. Fluid Mech.) on three circular cylinders in equilateral-triangular arrangement immersed in an incoming flow at Re=100. The optimal cylinder rotations lead to 44.0% net drag power saving with 85.8% drag reduction and 41.8% actuation power. The optimal results for active flow control based on this configuration have achieved boat-tailing mechanism by employing Coanda forcing and wake stabilization by delaying separation and minimizing the wake region.

Keywords: direct numerical simulations, flow control, kriging, stochastic optimization, wake stabilization

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Authors: B. Bouadjemi, S. Bentata, W. Benstaali, A. Abbad, T. Lantri, A. Zitouni

Abstract:

The purpose of this study was to investigate the structural,electronic and magnetic properties of the cubic praseodymium oxides perovskites PrMnO3. It includes our calculations based on the use of the density functional theory (DFT) with both generalized gradient approximation (GGA) and GGA+U approaches, The spin polarized electronic band structures and densities of states aswellas the integer value of the magnetic moment of the unit cell (6 μB) illustrate that PrMnO3 is half-metallic ferromagnetic. The study shows that the robust half-metallicity makes the cubic PrMnO3 a promising candidate for application in spintronics.

Keywords: Perovskite, DFT, electronic properties, Magnetic moment, half-metallic

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Authors: Amir Azaron

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In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain.

Keywords: supply chain management, stochastic programming, multiobjective programming, inventory control

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Abeer Amayri, Akif A. Bulgak

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Due to today’s globalization as well as outsourcing practices of the companies, the Supply Chain (SC) performances have become more dependent on the efficient movement of material among places that are geographically dispersed, where there is more chance for disruptions. One such disruption is the quality and delivery uncertainties of outsourcing. These uncertainties could lead the products to be unsafe and, as is the case in a number of recent examples, companies may have to end up in recalling their products. As a result of these problems, there is a need to develop a methodology for selecting suppliers globally in view of risks associated with low quality and late delivery. Accordingly, we developed a two-stage stochastic model that captures the risks associated with uncertainty in quality and delivery as well as a solution procedure for the model. The stochastic model developed simultaneously optimizes supplier selection and purchase quantities under price discounts over a time horizon. In particular, our target is the study of global organizations with multiple sites and multiple overseas suppliers, where the pricing is offered in suppliers’ local currencies. Our proposed methodology is applied to a case study for a US automotive company having two assembly plants and four potential global suppliers to illustrate how the proposed model works in practice.

Keywords: global supply chains, quality, stochastic programming, supplier selection

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Authors: A. Zitouni, S. Bentata, B. Bouadjemi, T. Lantri, W. Benstaali, A. Zoubir, S. Cherid, A. Sefir

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The structural, electronic, and magnetic properties of transition metal Co and Mn doped zinc-blende semiconductor CdTe were calculated using the density functional theory (DFT) with both generalized gradient approximation (GGA). We have analyzed the structural parameters, charge and spin densities, total and partial densities of states. We find that the Co and Mn doped zinc blende CdTe show half-metallic behavior with a total magnetic moment of 6.0 and 10.0 µB, respectively.The results obtained, make the Co and Mn doped CdTe a promising candidate for application in spintronics.

Keywords: first-principles, half-metallic, diluted magnetic semiconductor, magnetic moment

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Authors: Mohammed Belloufi, Rachid Benzine, Badreddine Sellami

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Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given.

Keywords: unconstrained optimization, conjugate gradient method, strong Wolfe line search, global convergence

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Authors: Tsegay Giday Woldu, Haibin Zhang, Xin Zhang, Yemane Hailu Fissuh

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It is well known that nonlinear conjugate gradient method is one of the widely used first order methods to solve large scale unconstrained smooth optimization problems. Because of the low memory requirement, attractive theoretical features, practical computational efficiency and nice convergence properties, nonlinear conjugate gradient methods have a special role for solving large scale unconstrained optimization problems. Large scale optimization problems are with important applications in practical and scientific world. However, nonlinear conjugate gradient methods have restricted information about the curvature of the objective function and they are likely less efficient and robust compared to some second order algorithms. To overcome these drawbacks, the new modified nonlinear conjugate gradient method is presented. The noticeable features of our work are that the new search direction possesses the sufficient descent property independent of any line search and it belongs to a trust region. Under mild assumptions and standard Wolfe line search technique, the global convergence property of the proposed algorithm is established. Furthermore, to test the practical computational performance of our new algorithm, numerical experiments are provided and implemented on the set of some large dimensional unconstrained problems. The numerical results show that the proposed algorithm is an efficient and robust compared with other similar algorithms.

Keywords: conjugate gradient method, global convergence, large scale optimization, sufficient descent property

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: noise, signal-to-noise ratio, stochastic signals, variance estimation

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Authors: Zhifeng Kong

Abstract:

Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: over-parameterization, rectified linear units ReLU, convergence, gradient descent, neural networks

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Authors: Zhongjie Yu, Hancheng Yu

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In this paper, we propose an effective method to detect concentric circles with imperfect edges. First, the gradient of edge pixel is coded and a 2-D lookup table is built to speed up normal generation. Then we take an accumulator to estimate the rough center and collect plausible edges of concentric circles through gradient and distance. Later, we take the contour-based method, which takes the contour and edge intersection, to pre-classify the edges. Finally, we use the extended RANSAC method to find all the candidate circles. The center of concentric circles is determined by the two circles with the highest concentricity. Experimental results demonstrate that the proposed method has both good performance and accuracy for the detection of concentric circles.

Keywords: concentric circle detection, gradient, contour, edge pre-classification, RANSAC

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time.

Keywords: mathematical expectation, filtration, anomalous noise, memory

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Authors: Seon Soon Choi

Abstract:

The essential purpose is to present the good fatigue crack propagation model describing a stochastic fatigue crack growth behavior in a rolled magnesium alloy, AZ31, under various load ratio conditions. Fatigue crack propagation experiments were carried out in laboratory air under four conditions of load ratio, R, using AZ31 to investigate the crack growth behavior. The stochastic fatigue crack growth behavior was analyzed using an interpolation of random variable, Z, introduced to an empirical fatigue crack propagation model. The empirical fatigue models used in this study are Paris-Erdogan model, Walker model, Forman model, and modified Forman model. It was found that the random variable is useful in describing the stochastic fatigue crack growth behaviors under various load ratio conditions. The good probabilistic model describing a stochastic fatigue crack growth behavior under various load ratio conditions was also proposed.

Keywords: magnesium alloys, fatigue crack propagation model, load ratio, interpolation of random variable

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Authors: A. Bentabet, A. Aydin, N. Fenineche

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In this work, we try to determine the best analytical approximation of differential cross sections, used generally in Monte Carlo simulation, to study the electron/positron slowing down in solid targets in the energy range up to 10 keV. Actually, our comparative study was carried out on the angular distribution of the scattering angle, the elastic total and the first transport cross sections which are the essential quantities used generally in the electron/positron transport study by using both stochastic and deterministic methods. Indeed, the obtained results using the relativistic partial wave expansion method and the backscattering coefficient experimental data are used as criteria to evaluate the used model.

Keywords: differential cross-section, backscattering coefficient, Rutherford cross-section, Vicanek and Urbassek theory

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Authors: O. W. Lawal, L. O. Ahmed, Y. K. Ali

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The unsteady MHD Poiseuille flow of a third grade fluid between two parallel horizontal nonconducting porous plates is studied with heat transfer. The two plates are fixed but maintained at different constant temperature with the Joule and viscous dissipation taken into consideration. The fluid motion is produced by a sudden uniform exponential decaying pressure gradient and external uniform magnetic field that is perpendicular to the plates. The momentum and energy equations governing the flow are solved numerically using Maple program. The effects of magnetic field and third grade fluid parameters on velocity and temperature profile are examined through several graphs.

Keywords: exponential decaying pressure gradient, MHD flow, Poiseuille flow, third grade fluid

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Authors: Danni Cong, Meiping Wu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokuncai, Hao Qin

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Gravity gradient instrument (GGI) is the core of the gravity gradiometer, so the structural error of the sensor has a great impact on the measurement results. In order not to affect the aimed measurement accuracy, limit error is required in the installation of the accelerometer. In this paper, based on the established measuring principle model, the radial installation limit error is calibrated, which is taken as an example to provide a method to calculate the other limit error of the installation under the premise of ensuring the accuracy of the measurement result. This method provides the idea for deriving the limit error of the geometry structure of the sensor, laying the foundation for the mechanical precision design and physical design.

Keywords: gravity gradient sensor, radial installation limit error, accelerometer, uniaxial rotational modulation

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

Abstract:

In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: Guillaume Leduc

Abstract:

In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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Authors: Navdeep Goel, Salvador Gabarda

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Digital images are widely used in computer applications. To store or transmit the uncompressed images requires considerable storage capacity and transmission bandwidth. Image compression is a means to perform transmission or storage of visual data in the most economical way. This paper explains about how images can be encoded to be transmitted in a multiplexing time-frequency domain channel. Multiplexing involves packing signals together whose representations are compact in the working domain. In order to optimize transmission resources each 4x4 pixel block of the image is transformed by a suitable polynomial approximation, into a minimal number of coefficients. Less than 4*4 coefficients in one block spares a significant amount of transmitted information, but some information is lost. Different approximations for image transformation have been evaluated as polynomial representation (Vandermonde matrix), least squares + gradient descent, 1-D Chebyshev polynomials, 2-D Chebyshev polynomials or singular value decomposition (SVD). Results have been compared in terms of nominal compression rate (NCR), compression ratio (CR) and peak signal-to-noise ratio (PSNR) in order to minimize the error function defined as the difference between the original pixel gray levels and the approximated polynomial output. Polynomial coefficients have been later encoded and handled for generating chirps in a target rate of about two chirps per 4*4 pixel block and then submitted to a transmission multiplexing operation in the time-frequency domain.

Keywords: chirp signals, image multiplexing, image transformation, linear canonical transform, polynomial approximation

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Authors: S. O. Oyamakin, A. U. Chukwu

Abstract:

Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Colin O’Hare, Zili Zho, Thomas Sneddon

Abstract:

The Australian superannuation system has received high praise for its participation rates and level of funding in retirement yet it is only 25 years old. In recent years, with increasing longevity and persistent lower rates of investment return, how adequate will the funds accumulated through a superannuation system be? In this paper we take Australia as a case study and build a stochastic model of accumulation and decummulation of funds and determine the expected number of years a fund may last an individual in retirement.

Keywords: component, mortality, stochastic models, superannuation

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Authors: Ian Marc G. Cabugsa, Kim Ryan A. Won

Abstract:

Fast, reliable and simultaneous HPLC analysis of theobromine and caffeine in cacao and cocoa products was optimized in this study. The samples tested were raw, fermented, and roasted cacao beans as well as commercially available cocoa products. The HPLC analysis was carried out using step gradient solvent system with acetonitrile and water buffered with H3PO4 as the mobile phase. The HPLC system was optimized using 273 nm wavelength at 35 °C for the column temperature with a flow rate of 1.0 mL/min. Using this method, the theobromine percent recovery mean, Limit of Detection (LOD) and Limit of Quantification (LOQ) is 118.68(±3.38)%, 0.727 and 1.05 respectively. The percent recovery mean, LOD and LOQ for caffeine is 105.53(±3.25)%, 2.42 and 3.50 respectively. The inter-day and intra-day precision for theobromine is 4.31% and 4.48% respectively, while 7.02% and 7.03% was for caffeine respectively. Compared to the standard method in AOAC using methanol in isocratic solvent system, the results of the study produced lesser chromatogram noise with emphasis on theobromine and caffeine. The method is readily usable for cacao and cocoa substances analyses using HPLC with step gradient capability.

Keywords: cacao, caffeine, HPLC, step gradient solvent system, theobromine

Procedia PDF Downloads 274