Search results for: linear and polynomial model.

Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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Authors: Giovanni Masala, Stefania Marica

Abstract:

Forecasting electricity load plays a crucial role regards decision making and planning for economical purposes. Besides, in the light of the recent privatization and deregulation of the power industry, the forecasting of future electricity load turned out to be a very challenging problem. Empirical data about electricity load highlights a clear seasonal behavior (higher load during the winter season), which is partly due to climatic effects. We also emphasize the presence of load periodicity at a weekly basis (electricity load is usually lower on weekends or holidays) and at daily basis (electricity load is clearly influenced by the hour). Finally, a long-term trend may depend on the general economic situation (for example, industrial production affects electricity load). All these features must be captured by the model. The purpose of this paper is then to build an hourly electricity load model. The deterministic component of the model requires non-linear regression and Fourier series while we will investigate the stochastic component through econometrical tools. The calibration of the parameters’ model will be performed by using data coming from the Italian market in a 6 year period (2007- 2012). Then, we will perform a Monte Carlo simulation in order to compare the simulated data respect to the real data (both in-sample and out-of-sample inspection). The reliability of the model will be deduced thanks to standard tests which highlight a good fitting of the simulated values.

Keywords: ARMA-GARCH process, electricity load, fitting tests, Fourier series, Monte Carlo simulation, non-linear regression.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

Abstract:

There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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Authors: Aref Ghafouri, Mohammad Javad Mollakazemi, Farhad Asadi

Abstract:

In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further.

Keywords: Frequency response, Order of model reduction, frequency matching condition.

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Authors: Zaineb Ben Messaoud, Dorra Gargouri, Saida Zribi, Ahmed Ben Hamida

Abstract:

This paper presents a formant-tracking linear prediction (FTLP) model for speech processing in noise. The main focus of this work is the detection of formant trajectory based on Hidden Markov Models (HMM), for improved formant estimation in noise. The approach proposed in this paper provides a systematic framework for modelling and utilization of a time- sequence of peaks which satisfies continuity constraints on parameter; the within peaks are modelled by the LP parameters. The formant tracking LP model estimation is composed of three stages: (1) a pre-cleaning multi-band spectral subtraction stage to reduce the effect of residue noise on formants (2) estimation stage where an initial estimate of the LP model of speech for each frame is obtained (3) a formant classification using probability models of formants and Viterbi-decoders. The evaluation results for the estimation of the formant tracking LP model tested in Gaussian white noise background, demonstrate that the proposed combination of the initial noise reduction stage with formant tracking and LPC variable order analysis, results in a significant reduction in errors and distortions. The performance was evaluated with noisy natual vowels extracted from international french and English vocabulary speech signals at SNR value of 10dB. In each case, the estimated formants are compared to reference formants.

Keywords: Formants Estimation, HMM, Multi Band Spectral Subtraction, Variable order LPC coding, White Gauusien Noise.

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Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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Authors: G. Parmar, R. Prasad, S. Mukherjee

Abstract:

The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

Keywords: Genetic algorithm, Integral square error, Orderreduction, Stability equation method.

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Authors: Jer-Rong Chang

Abstract:

The flexible follower response of a translating cam with four different profiles for rise-dwell-fall-dwell (RDFD) motion is investigated. The cycloidal displacement motion, the modified sinusoidal acceleration motion, the modified trapezoidal acceleration motion, and the 3-4-5 polynomial motion are employed to describe the rise and the fall motions of the follower and the associated four kinds of cam profiles are studied. Since the follower flexibility is considered, the contact point of the roller and the cam is an unknown. Two geometric constraints formulated to restrain the unknown position are substituted into Hamilton-s principle with Lagrange multipliers. Applying the assumed mode method, one can obtain the governing equations of motion as non-linear differential-algebraic equations. The equations are solved using Runge-Kutta method. Then, the responses of the flexible follower undergoing the four different motions are investigated in time domain and in frequency domain.

Keywords: translating cam, flexible follower, rise-dwell-falldwell, response

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Authors: L. Basha, E. Gjika

Abstract:

This study is focused on analyzing climate change in Albania and its potential effects on cereal yields. Initially, monthly temperature and rainfalls in Albania were studied for the period 1960-2021. Climacteric variables are important variables when trying to model cereal yield behavior, especially when significant changes in weather conditions are observed. For this purpose, in the second part of the study, linear and nonlinear models explaining cereal yield are constructed for the same period, 1960-2021. The multiple linear regression analysis and lasso regression method are applied to the data between cereal yield and each independent variable: average temperature, average rainfall, fertilizer consumption, arable land, land under cereal production, and nitrous oxide emissions. In our regression model, heteroscedasticity is not observed, data follow a normal distribution, and there is a low correlation between factors, so we do not have the problem of multicollinearity. Machine learning methods, such as Random Forest (RF), are used to predict cereal yield responses to climacteric and other variables. RF showed high accuracy compared to the other statistical models in the prediction of cereal yield. We found that changes in average temperature negatively affect cereal yield. The coefficients of fertilizer consumption, arable land, and land under cereal production are positively affecting production. Our results show that the RF method is an effective and versatile machine-learning method for cereal yield prediction compared to the other two methods: multiple linear regression and lasso regression method.

Keywords: Cereal yield, climate change, machine learning, multiple regression model, random forest.

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Authors: S. H. Nasseri, M. Sohrabi, E. Ardil

Abstract:

In this paper, we give a certain decomposition of the coefficient matrix of the fully fuzzy linear system (FFLS) to obtain a simple algorithm for solving these systems. The new algorithm can solve FFLS in a smaller computing process. We will illustrate our method by solving some examples.

Keywords: Fully fuzzy linear system, Fuzzy number, LUdecomposition.

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Authors: A. M. Pashayev, D. D. Askerov, C. Ardil, R. A. Sadiqov, P. S. Abdullayev

Abstract:

Researches show that probability-statistical methods application, especially at the early stage of the aviation Gas Turbine Engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods is considered. According to the purpose of this problem training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. For GTE technical condition more adequate model making dynamics of skewness and kurtosis coefficients- changes are analysed. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE workand output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stage-by-stage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine technical condition was made.

Keywords: aviation gas turbine engine, technical condition, fuzzy logic, neural networks, fuzzy statistics

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, application of Sliding Mode Control (SMC) technique for an Active Magnetic Bearing (AMB) system with varying rotor speed is considered. The gyroscopic effect and mass imbalance inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Transformation of the AMB dynamic model into regular system shows that these gyroscopic effect and imbalance lie in the mismatched part of the system. A H2-based sliding surface is designed which bound the mismatched parts. The solution of the surface parameter is obtained using Linear Matrix Inequality (LMI). The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active magnetic bearing, sliding mode control, linear matrix inequality, mismatched uncertainty and imbalance.

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

Abstract:

This paper aims to analysis the behavior of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Currentvoltage curves are particularly analyzed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: Electrostatic precipitator, current-voltage characteristics, Least Squares method, electric field, magnetic field.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

Abstract:

Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

Abstract:

Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: A. Abdikian

Abstract:

A quantum breathing mode has been theatrically studied in quantum dusty plasma. By using linear quantum hydrodynamic model, not only the quantum dispersion relation of rotation mode but also void structure has been derived in the presence of an external magnetic field. Although the phase velocity of the magnetized quantum breathing mode is greater than that of unmagnetized quantum breathing mode, attenuation of the magnetized quantum breathing mode along radial distance seems to be slower than that of unmagnetized quantum breathing mode. Clearly, drawing the quantum breathing mode in the presence and absence of a magnetic field, we found that the magnetic field alters the distribution of dust particles and changes the radial and azimuthal velocities around the axis. Because the magnetic field rotates the dust particles and collects them, it could compensate the void structure.

Keywords: The linear quantum hydrodynamic model, the magnetized quantum breathing mode, the quantum dispersion relation of rotation mode, void structure.

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Authors: Sara Barati, Karim Ivaz

Abstract:

In this paper, using a model transformation approach a system of linear delay differential equations (DDEs) with multiple delays is converted to a non-delayed initial value problem. The variational iteration method (VIM) is then applied to obtain the approximate analytical solutions. Numerical results are given for several examples involving scalar and second order systems. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that this method is very effective and convenient.

Keywords: Variational iteration method, delay differential equations, multiple delays, Runge-Kutta method.

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Authors: B. M. Mohan, Sanjeeb Kumar Kar

Abstract:

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

Keywords: Linear quadratic Gaussian control, linear quadratic estimator, linear quadratic regulator, time-invariant systems, orthogonal functions, block-pulse functions, shifted legendre polynomials.

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Authors: Yusoff Y. S., Streftaris, G., Waters, H. R

Abstract:

Death within 30 days is an important factor to be looked into, as there is a significant risk of deaths immediately following or soon after, myocardial infarction (MI) or stroke. In this paper, we will model the deaths within 30 days following a myocardial infarction (MI) or stroke in the UK. We will see how the probabilities of sudden deaths from MI or stroke have changed over the period 1981-2000. We will model the sudden deaths using a generalized linear model (GLM), fitted using the R statistical package, under a Binomial distribution for the number of sudden deaths. We parameterize our model using the extensive and detailed data from the Framingham Heart Study, adjusted to match UK rates. The results show that there is a reduction for the sudden deaths following a MI over time but no significant improvement for sudden deaths following a stroke.

Keywords: Sudden deaths, myocardial infarction, stroke, ischemic heart disease.

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Authors: Adriano Z. Zambom, Preethi Ravikumar

Abstract:

One of the biggest challenges in nonparametric regression is the curse of dimensionality. Additive models are known to overcome this problem by estimating only the individual additive effects of each covariate. However, if the model is misspecified, the accuracy of the estimator compared to the fully nonparametric one is unknown. In this work the efficiency of completely nonparametric regression estimators such as the Loess is compared to the estimators that assume additivity in several situations, including additive and non-additive regression scenarios. The comparison is done by computing the oracle mean square error of the estimators with regards to the true nonparametric regression function. Then, a backward elimination selection procedure based on the Akaike Information Criteria is proposed, which is computed from either the additive or the nonparametric model. Simulations show that if the additive model is misspecified, the percentage of time it fails to select important variables can be higher than that of the fully nonparametric approach. A dimension reduction step is included when nonparametric estimator cannot be computed due to the curse of dimensionality. Finally, the Boston housing dataset is analyzed using the proposed backward elimination procedure and the selected variables are identified.

Keywords: Additive models, local polynomial regression, residuals, mean square error, variable selection.

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Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: Shan-Jen Cheng, Te-Jen Chang, Kuang-Hsiung Tan, Shou-Ling Kuo

Abstract:

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accuracy of NNARX model are tested by one step ahead relating output voltage to input current from measured experimental of PEMFC. The results show that the obtained nonlinear NNARX model can efficiently approximate the dynamic mode of the PEMFC and model output and system measured output consistently.

Keywords: PEMFC, neural network, nonlinear identification, NNARX.

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Authors: Kejun Zhuang, Hailong Zhu

Abstract:

The dynamics of a delayed mathematical model for Hes1 oscillatory expression are investigated. The linear stability of positive equilibrium and existence of local Hopf bifurcation are studied. Moreover, the global existence of large periodic solutions has been established due to the global bifurcation theorem.

Keywords: Hes1, Hopf bifurcation, time delay, transcriptional repression loop

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Authors: Ramaswamy Palaniappan

Abstract:

In this paper, a second order autoregressive (AR) model is proposed to discriminate alcoholics using single trial gamma band Visual Evoked Potential (VEP) signals using 3 different classifiers: Simplified Fuzzy ARTMAP (SFA) neural network (NN), Multilayer-perceptron-backpropagation (MLP-BP) NN and Linear Discriminant (LD). Electroencephalogram (EEG) signals were recorded from alcoholic and control subjects during the presentation of visuals from Snodgrass and Vanderwart picture set. Single trial VEP signals were extracted from EEG signals using Elliptic filtering in the gamma band spectral range. A second order AR model was used as gamma band VEP exhibits pseudo-periodic behaviour and second order AR is optimal to represent this behaviour. This circumvents the requirement of having to use some criteria to choose the correct order. The averaged discrimination errors of 2.6%, 2.8% and 11.9% were given by LD, MLP-BP and SFA classifiers. The high LD discrimination results show the validity of the proposed method to discriminate between alcoholic subjects.

Keywords: Linear Discriminant, Neural Network, VisualEvoked Potential.

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Authors: A. Moussouni, L. Mouzai, M. Bouhadef

Abstract:

The purpose of this investigation is to relate the rain power and the overland flow power to soil erodibility to assess the effects of both parameters on soil erosion using variable rainfall intensity on remoulded agricultural soil. Six rainfall intensities were used to simulate the natural rainfall and are as follows: 12.4mm/h, 20.3mm/h, 28.6mm/h, 52mm/h, 73.5mm/h and 103mm/h. The results have shown that the relationship between overland flow power and rain power is best represented by a linear function (R2=0.99). As regards the relationships between soil erodibility factor and rain and overland flow powers, the evolution of both parameters with the erodibility factor follow a polynomial function with high coefficient of determination. From their coefficients of determination (R2=0.95) for rain power and (R2=0.96) for overland flow power, we can conclude that the flow has more power to detach particles than rain. This could be explained by the fact that the presence of particles, already detached by rain and transported by the flow, give the flow more weight and then contribute to the detachment of particles by collision.

Keywords: Laboratory experiments, soil erosion, flow power, erodibility, rainfall intensity.

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