Search results for: Universal Approximation function

Authors: Yong-Taeg Oh, Won Song, Seok-Eui Choi, Bo-Ra Koo, Dong-Chan Shin

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ZnO+Ga2O3 functionally graded thin films (FGTFs) were examined for their potential use as Solar cell and organic light emitting diodes (OLEDs). FGTF transparent conducting oxides (TCO) were fabricated by combinatorial RF magnetron sputtering. The composition gradient was controlled up to 10% by changing the plasma power of the two sputter guns. A Ga2O3+ZnO graded region was placed on the top layer of ZnO. The FGTFs showed up to 80% transmittance. Their surface resistances were reduced to < 10% by increasing the Ga2O3: pure ZnO ratio in the TCO. The FGTFs- work functions could be controlled within a range of 0.18 eV. The controlled work function is a very promising technology because it reduces the contact resistance between the anode and Hall transport layers of OLED and solar cell devices.

Keywords: Work Function, TCO, Functionally Graded Thin Films, Resistance, Transmittance.

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Authors: Yongxin Yuan

Abstract:

The problem of updating damped gyroscopic systems using measured modal data can be mathematically formulated as following two problems. Problem I: Given Ma ∈ Rn×n, Λ = diag{λ1, ··· , λp} ∈ Cp×p, X = [x1, ··· , xp] ∈ Cn×p, where p<n and both Λ and X are closed under complex conjugation in the sense that λ2j = λ¯2j−1 ∈ C, x2j = ¯x2j−1 ∈ Cn for j = 1, ··· , l, and λk ∈ R, xk ∈ Rn for k = 2l + 1, ··· , p, find real-valued symmetric matrices D,K and a real-valued skew-symmetric matrix G (that is, GT = −G) such that MaXΛ2 + (D + G)XΛ + KX = 0. Problem II: Given real-valued symmetric matrices Da, Ka ∈ Rn×n and a real-valued skew-symmetric matrix Ga, find (D, ˆ G, ˆ Kˆ ) ∈ SE such that Dˆ −Da2+Gˆ−Ga2+Kˆ −Ka2 = min(D,G,K)∈SE (D− Da2 + G − Ga2 + K − Ka2), where SE is the solution set of Problem I and · is the Frobenius norm. This paper presents an iterative algorithm to solve Problem I and Problem II. By using the proposed iterative method, a solution of Problem I can be obtained within finite iteration steps in the absence of roundoff errors, and the minimum Frobenius norm solution of Problem I can be obtained by choosing a special kind of initial matrices. Moreover, the optimal approximation solution (D, ˆ G, ˆ Kˆ ) of Problem II can be obtained by finding the minimum Frobenius norm solution of a changed Problem I. A numerical example shows that the introduced iterative algorithm is quite efficient.

Keywords: Model updating, iterative algorithm, gyroscopic system, partially prescribed spectral data, optimal approximation.

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Authors: Yuri Boiko, Iluju Kiringa, Tet Yeap

Abstract:

Current drainage attack suggested previously is further studied in regular settings of closed-loop controlled Brushless DC (BLDC) motor with Kalman filter in the feedback loop. Modeling and simulation experiments are conducted in a MATLAB environment, implementing the closed-loop control model of BLDC motor operation in position sensorless mode under Kalman filter drive. The current increase in the motor windings is caused by the controller (p-controller in our case) affected by false data injection of substitution of the angular velocity estimates with distorted values. Operation of multiplication to distortion coefficient, values of which are taken from the distortion function synchronized in its periodicity with the rotor’s position change. A saw function with a triangular tooth shape is studied herewith for the purpose of carrying out the bias injection with current drainage consequences. The specific focus here is on how the asymmetry of the tooth in the saw function affects the flow of current drainage. The purpose is two-fold: (i) to produce and collect the signature of an asymmetric saw in the attack for further pattern recognition process, and (ii) to determine conditions of improving stealthiness of such attack via regulating asymmetry in saw function used. It is found that modification of the symmetry in the saw tooth affects the periodicity of current drainage modulation. Specifically, the modulation frequency of the drained current for a fully asymmetric tooth shape coincides with the saw function modulation frequency itself. Increasing the symmetry parameter for the triangle tooth shape leads to an increase in the modulation frequency for the drained current. Moreover, such frequency reaches the switching frequency of the motor windings for fully symmetric triangular shapes, thus becoming undetectable and improving the stealthiness of the attack. Therefore, the collected signatures of the attack can serve for attack parameter identification via the pattern recognition route.

Keywords: Bias injection attack, Kalman filter, BLDC motor, control system, closed loop, P-controller, PID-controller, current drainage, saw-function, asymmetry.

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Authors: Rongtao Ding, Xinhao Ji, Linting Zhu

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In recent years, the relevance feedback technology is regarded in content-based image retrieval. This paper suggests a neural networks feedback algorithm based on the radial basis function, coming to extract the semantic character of image. The results of experiment indicated that the performance of this relevance feedback is better than the feedback algorithm based on Single-RBF.

Keywords: Image retrieval, relevance feedback, radial basis function.

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Authors: Mahasen M. Abdel-Mageed, H. S. Zaghloul

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Annihilations, phase shifts, scattering lengths and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wave function is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical and experimental results. Especially, the estimated positive scattering length supports the possibility of positronmagnesium bound state system that was confirmed in previous experimental and theoretical work.

Keywords: Bound wave function, Positron Annihilation, scattering phase shift, scattering length.

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Authors: Miklos Palfia

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An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.

Keywords: Means, matrix means, operator means, geometric mean, Riemannian center of mass.

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Authors: Dimitris Varsamis, Christos Talagkozis, Alkiviadis Tsimpiris, Paris Mastorocostas

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The aim of this work is the parallel implementation of k-means in MATLAB, in order to reduce the execution time. Specifically, a new function in MATLAB for serial k-means algorithm is developed, which meets all the requirements for the conversion to a function in MATLAB with parallel computations. Additionally, two different variants for the definition of initial values are presented. In the sequel, the parallel approach is presented. Finally, the performance tests for the computation times respect to the numbers of features and classes are illustrated.

Keywords: K-means algorithm, clustering, parallel computations, MATLAB.

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Authors: Ryad Zemouri, Paul Ciprian Patic

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An adaptive software reliability prediction model using evolutionary connectionist approach based on Recurrent Radial Basis Function architecture is proposed. Based on the currently available software failure time data, Fuzzy Min-Max algorithm is used to globally optimize the number of the k Gaussian nodes. The corresponding optimized neural network architecture is iteratively and dynamically reconfigured in real-time as new actual failure time data arrives. The performance of our proposed approach has been tested using sixteen real-time software failure data. Numerical results show that our proposed approach is robust across different software projects, and has a better performance with respect to next-steppredictability compared to existing neural network model for failure time prediction.

Keywords: Neural network, Prediction error, Recurrent RadialBasis Function Network, Reliability prediction.

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Authors: Merve Gücen

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One of the aims of education is to educate individuals who have embraced universal moral principles and transform universal moral principles into moral values. Character education aims to educate behaviors of individuals in their mental activities to transform moral principles into moral values in their lives. As the result of this education, individuals are expected to develop positive character traits and become morally indifferent individuals. What are the characteristics of the factors that influence character education at this stage? How should character education help individuals develop positive character traits? Which methods are more effective? These questions come to mind when studying character education. Our research was developed within the framework of these questions. The aim of our study is to provide the most effective use of the education factor that affects character. In this context, we tried to explain character definition, character development, character education and the factors affecting character education using qualitative research methods. At this stage, character education programs applied in various countries were examined and a character education program consisting of Islamic values was prepared and implemented in an International Imam Hatip High School in Istanbul. Our application was carried out with the collaboration of school and families. Various seminars were organized in the school and participation of families was ensured. In the last phase of our study, we worked with the students and their families on the effectiveness of the events held during the program. In this study, it was found that activities such as storytelling and theater in character education programs were effective in recognizing wrong behaviors in individuals. It was determined that our program had a positive effect on the quality of education. It was seen that applications of this educational program affected the behavior of the employees in the educational institution.

Keywords: Character development, values education, family activities, education program.

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Authors: Young-Seok Choi

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We present a family of data-reusing and affine projection algorithms. For identification of a noisy linear finite impulse response channel, a partial knowledge of a channel, especially noise, can be used to improve the performance of the adaptive filter. Motivated by this fact, the proposed scheme incorporates an estimate of a knowledge of noise. A constraint, called the adaptive noise constraint, estimates an unknown information of noise. By imposing this constraint on a cost function of data-reusing and affine projection algorithms, a cost function based on the adaptive noise constraint and Lagrange multiplier is defined. Minimizing the new cost function leads to the adaptive noise constrained (ANC) data-reusing and affine projection algorithms. Experimental results comparing the proposed schemes to standard data-reusing and affine projection algorithms clearly indicate their superior performance.

Keywords: Data-reusing, affine projection algorithm, error constraint, system identification.

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Authors: Prasit Wonglersak, Prakarnkiat Youngkong, Ittipon Cheowanish

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This paper aims to improve a fine lapping process of hard disk drive (HDD) lapping machines by removing materials from each slider together with controlling the strip height (SH) variation to minimum value. The standard deviation is the key parameter to evaluate the strip height variation, hence it is minimized. In this paper, a design of experiment (DOE) with factorial analysis by twoway analysis of variance (ANOVA) is adopted to obtain a statistically information. The statistics results reveal that initial stripe height patterns affect the final SH variation. Therefore, initial SH classification using a radial basis function neural network is implemented to achieve the proportional gain prediction.

Keywords: Stripe height variation, Two-way analysis ofvariance (ANOVA), Radial basis function neural network, Proportional gain prediction.

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Authors: Linjun Wu, Shihua Zhu, Xingle Feng

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In Orthogonal Frequency Division Multiplexing (OFDM) systems, the peak to average power ratio (PAR) is much high. The clipping signal scheme is a useful method to reduce PAR. Clipping the OFDM signal, however, increases the overall noise level by introducing clipping noise. It is necessary to recover the figure of the original signal at receiver in order to reduce the clipping noise. Considering the continuity of the signal and the figure of the peak, we obtain a certain conic function curve to replace the clipped signal module within the clipping time. The results of simulation show that the proposed scheme can reduce the systems? BER (bit-error rate) 10 times when signal-to-interference-and noise-ratio (SINR) equals to 12dB. And the BER performance of the proposed scheme is superior to that of kim's scheme, too.

Keywords: Orthogonal Frequency Division Multiplexing, Peak-to-Average Power Ratio, clipping time, conic function.

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Authors: Nur Zakiah Mohd Saat, Abdul Aziz Jemain

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Saddlepoint approximations is one of the tools to obtain an expressions for densities and distribution functions. We approximate the densities of the observed gaps between the hypopnea events using the Huzurbazar saddlepoint approximation. We demonstrate the density of a maximum likelihood estimator in exponential families.

Keywords: Exponential, maximum likehood estimators, observed gap, Saddlepoint approximations.

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Authors: R. Oonsivilai, A. Oonsivilai

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Realistic systems generally are systems with various inputs and outputs also known as Multiple Input Multiple Output (MIMO). Such systems usually prove to be complex and difficult to model and control purposes. Therefore, decomposition was used to separate individual inputs and outputs. A PID is assigned to each individual pair to regulate desired settling time. Suitable parameters of PIDs obtained from Genetic Algorithm (GA), using Mean of Squared Error (MSE) objective function.

Keywords: Gas Turbine, PID, Genetic Algorithm, Transfer function.Mean of Squared Error

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Authors: Domenica Tambasco, Riina Bray

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Fibromyalgia is a chronic condition characterized by widespread musculoskeletal pain, fatigue, and reduced function. Management of symptoms include medications, physical treatments and mindfulness therapies. Myofascial Release is a modality that has been successfully applied in various musculoskeletal conditions. However, to the author’s best knowledge, it is not yet recognized as a self-management therapy option in Fibromyalgia. In this study, we investigated whether Self-applied Myofascial Release (SMR) is associated with overall improved function and symptoms in Fibromyalgia. Eligible adult patients with a confirmed diagnosis of Fibromyalgia at Women’s College Hospital were recruited to SMR. Sessions ran for 1 hour once a week for 7 weeks, led by the same two physiotherapists knowledgeable in this physical treatment modality. The main outcome measure was an overall impact score for function and symptoms based on the validated assessment tool for fibromyalgia, the Revised Fibromyalgia Impact Questionnaire (FIQR), measured pre- and post-intervention. Both descriptive and analytical methods were applied and reported. We analyzed results using a paired t-test to determine if there was a statistically significant difference in mean FIQR scores between initial (pre-intervention) and final (post-intervention) scores. A clinically significant difference in FIQR was defined as a reduction in score by 10 or more points. Our pilot study showed that SMR appeared to be a safe and effective intervention for our fibromyalgia participants and the overall impact on function and symptoms occurred in only 7 weeks. Further studies with larger sample sizes comparing SMR to other physical treatment modalities (such as stretching) in an randomized control trial (RCT) are recommended.

Keywords: Fibromyalgia, myofascial release, fibromyalgia impact questionnaire, fibromyalgia assessment status.

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Authors: S. Anna Durai, E. Anna Saro

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In general the images used for compression are of different types like dark image, high intensity image etc. When these images are compressed using Counter Propagation Neural Network, it takes longer time to converge. The reason for this is that the given image may contain a number of distinct gray levels with narrow difference with their neighborhood pixels. If the gray levels of the pixels in an image and their neighbors are mapped in such a way that the difference in the gray levels of the neighbor with the pixel is minimum, then compression ratio as well as the convergence of the network can be improved. To achieve this, a Cumulative Distribution Function is estimated for the image and it is used to map the image pixels. When the mapped image pixels are used the Counter Propagation Neural Network yield high compression ratio as well as it converges quickly.

Keywords: Correlation, Counter Propagation Neural Networks, Cummulative Distribution Function, Image compression.

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Authors: Maumita Bhattacharya

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Optimization is often a critical issue for most system design problems. Evolutionary Algorithms are population-based, stochastic search techniques, widely used as efficient global optimizers. However, finding optimal solution to complex high dimensional, multimodal problems often require highly computationally expensive function evaluations and hence are practically prohibitive. The Dynamic Approximate Fitness based Hybrid EA (DAFHEA) model presented in our earlier work [14] reduced computation time by controlled use of meta-models to partially replace the actual function evaluation by approximate function evaluation. However, the underlying assumption in DAFHEA is that the training samples for the meta-model are generated from a single uniform model. Situations like model formation involving variable input dimensions and noisy data certainly can not be covered by this assumption. In this paper we present an enhanced version of DAFHEA that incorporates a multiple-model based learning approach for the SVM approximator. DAFHEA-II (the enhanced version of the DAFHEA framework) also overcomes the high computational expense involved with additional clustering requirements of the original DAFHEA framework. The proposed framework has been tested on several benchmark functions and the empirical results illustrate the advantages of the proposed technique.

Keywords: Evolutionary algorithm, Fitness function, Optimization, Meta-model, Stochastic method.

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Authors: Eleni Aggelogiannaki, Haralambos Sarimveis

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In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.

Keywords: Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.

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Authors: Rana Yousef, Khalil el Hindi

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The behavior of Radial Basis Function (RBF) Networks greatly depends on how the center points of the basis functions are selected. In this work we investigate the use of instance reduction techniques, originally developed to reduce the storage requirements of instance based learners, for this purpose. Five Instance-Based Reduction Techniques were used to determine the set of center points, and RBF networks were trained using these sets of centers. The performance of the RBF networks is studied in terms of classification accuracy and training time. The results obtained were compared with two Radial Basis Function Networks: RBF networks that use all instances of the training set as center points (RBF-ALL) and Probabilistic Neural Networks (PNN). The former achieves high classification accuracies and the latter requires smaller training time. Results showed that RBF networks trained using sets of centers located by noise-filtering techniques (ALLKNN and ENN) rather than pure reduction techniques produce the best results in terms of classification accuracy. The results show that these networks require smaller training time than that of RBF-ALL and higher classification accuracy than that of PNN. Thus, using ALLKNN and ENN to select center points gives better combination of classification accuracy and training time. Our experiments also show that using the reduced sets to train the networks is beneficial especially in the presence of noise in the original training sets.

Keywords: Radial basis function networks, Instance-based reduction, PNN.

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Authors: Deng Shiwei

Abstract:

The users are now expecting higher level of DSP(Digital Signal Processing) software quality than ever before. Prevention and detection of defect are critical elements of software quality assurance. In this paper, principles and rules for prevention and detection of defect are suggested, which are not universal guidelines, but are useful for both novice and experienced DSP software developers.

Keywords: defect detection, defect prevention, DSP-software, software development, software testing.

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Authors: Loai AbdAllah, Mahmoud Kaiyal

Abstract:

Missing values in real-world datasets are a common problem. Many algorithms were developed to deal with this problem, most of them replace the missing values with a fixed value that was computed based on the observed values. In our work, we used a distance function based on Bhattacharyya distance to measure the distance between objects with missing values. Bhattacharyya distance, which measures the similarity of two probability distributions. The proposed distance distinguishes between known and unknown values. Where the distance between two known values is the Mahalanobis distance. When, on the other hand, one of them is missing the distance is computed based on the distribution of the known values, for the coordinate that contains the missing value. This method was integrated with Wikaya, a digital health company developing a platform that helps to improve prevention of chronic diseases such as diabetes and cancer. In order for Wikaya’s recommendation system to work distance between users need to be measured. Since there are missing values in the collected data, there is a need to develop a distance function distances between incomplete users profiles. To evaluate the accuracy of the proposed distance function in reflecting the actual similarity between different objects, when some of them contain missing values, we integrated it within the framework of k nearest neighbors (kNN) classifier, since its computation is based only on the similarity between objects. To validate this, we ran the algorithm over diabetes and breast cancer datasets, standard benchmark datasets from the UCI repository. Our experiments show that kNN classifier using our proposed distance function outperforms the kNN using other existing methods.

Keywords: Missing values, distance metric, Bhattacharyya distance.

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Authors: Kai-Thorsten Wirt

Abstract:

In this paper we present the design of a new encryption scheme. The scheme we propose is a very exible encryption and authentication primitive. We build this scheme on two relatively new design principles: t-functions and fast pseudo hadamard transforms. We recapitulate the theory behind these principles and analyze their security properties and efficiency. In more detail we propose a streamcipher which outputs a message authentication tag along with theencrypted data stream with only little overhead. Moreover we proposesecurity-speed tradeoffs. Our scheme is faster than other comparablet-function based designs while offering the same security level.

Keywords: Cryptography, Combined Primitives, Stream Cipher, MAC, T-Function, FPHT.

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Authors: Sheroz Khan, A. F. Salami, W. A. Lawal, AHM Zahirul Alam, Shihab Abdel Hameed, M. J. E.Salami

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In this paper, a multi-branch power line is modeled using ABCD matrix to show its worth as a communication channel. The model is simulated using MATLAB in an effort to investigate the effects of multiple loading, multipath, and those as a result of load mismatching. The channel transfer function is obtained and investigated using different cable lengths, and different number of bridge taps under given loading conditions.

Keywords: Power line Communication, Transfer Function, Channel Modeling, Signal Transmission.

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Authors: Sung Hoon Jung

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In this paper, we propose a selective mutation method for improving the performances of genetic algorithms. In selective mutation, individuals are first ranked and then additionally mutated one bit in a part of their strings which is selected corresponding to their ranks. This selective mutation helps genetic algorithms to fast approach the global optimum and to quickly escape local optima. This results in increasing the performances of genetic algorithms. We measured the effects of selective mutation with four function optimization problems. It was found from extensive experiments that the selective mutation can significantly enhance the performances of genetic algorithms.

Keywords: Genetic algorithm, selective mutation, function optimization

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Authors: Jafar Biazar, Behzad Ghanbari

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In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

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Authors: Anant Oonsivilai, Sanom Saichoomdee

Abstract:

To determine the presence and location of faults in a transmission by the adaptation of protective distance relay based on the measurement of fixed settings as line impedance is achieved by several different techniques. Moreover, a fast, accurate and robust technique for real-time purposes is required for the modern power systems. The appliance of radial basis function neural network in transmission line protection is demonstrated in this paper. The method applies the power system via voltage and current signals to learn the hidden relationship presented in the input patterns. It is experiential that the proposed technique is competent to identify the particular fault direction more speedily. System simulations studied show that the proposed approach is able to distinguish the direction of a fault on a transmission line swiftly and correctly, therefore suitable for the real-time purposes.

Keywords: radial basis function neural network, transmission lines protection, relaying, power system.

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Authors: Rehana Naz, D. P. Mason, Fazal Mahomed

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A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl-s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the two velocity components. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the axisymmetric liquid and free jet. The multiplier approach applied to the third-order partial differential equation for the stream function yields two local conserved vectors one of which is a non-local conserved vector for the system. One of the conserved vectors gives the conserved quantity for the axisymmetric free jet but the conserved quantity for the wall jet is not obtained from the second conserved vector. The conserved quantity for the axisymmetric wall jet is derived from a non-local conserved vector of the third-order partial differential equation for the stream function. This non-local conserved vector for the third-order partial differential equation for the stream function is obtained by using the stream function as multiplier.

Keywords: Axisymmetric jet, liquid jet, free jet, wall jet, conservation laws, conserved quantity.

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Authors: Mohamed K. El Daou

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We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

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Authors: Helyane B. Borges, Julio Cesar Nievola

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Hierarchical classification is a problem with applications in many areas as protein function prediction where the dates are hierarchically structured. Therefore, it is necessary the development of algorithms able to induce hierarchical classification models. This paper presents experimenters using the algorithm for hierarchical classification called Multi-label Hierarchical Classification using a Competitive Neural Network (MHC-CNN). It was tested in ten datasets the Gene Ontology (GO) Cellular Component Domain. The results are compared with the Clus-HMC and Clus-HSC using the hF-Measure.

Keywords: Hierarchical Classification, Competitive Neural Network, Global Classifier.

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Authors: Minghui Wang, Luping Xu, Juntao Zhang

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Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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