Abstract- In this paper proposed blotches and impulse removal in color scale images using **nonlinear** decision based **algorithm**. The implementation of this **algorithm** can be obtained by **two** stages. In first **stage** the pixel are detected as corrupted / uncorrupted using decision rules. In second **stage** estimate the new pixel value for corrupted pixels. The **algorithm** used as a adaptive length window whose maximum size is 5X5 to avoid blurring due to large window sizes. The mean filtering is automatically switched in this proposed **algorithm**. It also tests the different images. To analyze the performance of this **algorithm** as mean square error, peak signal to noise ratio, computation time and image enhancement factor compare to other **algorithm**. The noise level is effectively removal without any loss it produces the better result in quantitative and qualitative measures of the image and also provides better performance.

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The INLP model can be obtained a local optimal solution by using LINGO software’s **nonlinear** option with very long CPU time. However, the local solution is not the global one, and there also has some chance to improve the solution, meanwhile practical decisions could not wait for long calculating time. Therefore, it is necessary to develop an **algorithm** that can search an optimal solution for the INLP model within a reasonable CPU time in robustness. Since the objective of the INLP model is to find a minimum supply chain cost, we propose a heuristic **algorithm** that starts from any feasible initial solution, and finally get an optimal solution by adjusting the suppliers’ supplying quantity according to their unit costs step by step, and name the **algorithm** as Unit Cost Adjusting (UCA) heuristic.

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Abstract: The power-voltage (P-V) characteristic curves of a PV array are **nonlinear** and have multiple peaks under partially shaded conditions (PSCs). This paper proposes a novel maximum power point tracking (MPPT) method for a PV system with reduced steady-state oscillation based on a **two**-**stage** particle swarm optimization (PSO) **algorithm**. The grouping method of the shuffled frog leaping **algorithm** (SFLA) is incorporated in the basic PSO **algorithm** (PSO-SFLA), ensuring fast and accurate searching of the global extremum. An adaptive speed factor is also introduced into the improved PSO to further enhance its convergence speed. Tests results show that the proposed method converges in less than half the time taken by the conventional PSO method, and the power is improved by 33% under the worst PSCs, which confirms the superiority of the proposed method over the standard PSO **algorithm** in terms of tracking speed and steady-state oscillations under different PSCs.

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Previous research in using single-**stage** bootstrapping for relation extraction has been focusing on relations which are specific and do not seem to contain subtypes of relations. However, there are many other relations which are really a set of relations. Take EMP-ORG for example; it contains at least 3 different types of relations, executive-organization, staff-organization and other-organization (where the contexts are not sufficient enough to determine whether a person holds a managerial or general staff position in the organization). One can imagine that, compared to the organization-headquarters relation, there are more diverse ways of stating employment than headquarters of organizations. In particular, relation patterns for EMP- ORG involve more relation nominals including executive, head, manager, programmer, editor and many others. Suppose we start with the seed Bill Gates and Microsoft; a simple question for single-**stage** bootstrapping is how could we learn nominal patterns with economist or editor, involving words other than synonyms of the position of Bill Gates such as CEO, chairman or head?

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In practice, the problem parameters associated with the dynamic capacity ac- quisition and assignment problem (1) are rarely known with complete certainty. To incorporate uncertainty in the decision making process, we adopt a **two**-**stage** stochastic programming approach [3]. We assume that the capacity planning decisions (for the entire planning horizon) have to made here and now, with only some knowledge of future scenarios of task processing requirements and the processing costs. Once the capacities are decided, time unfolds and a cer- tain scenario of the problem parameters realizes, and then the optimal decision regarding the task-resource assignment is made. The overall objective is to de- termine a capacity acquisition plan, such that the sum of acquisition cost and the expected assignment costs is minimized. Note that although the problem is a multi-period one, since the capacity planning decisions for all periods are made in period one, the problem is essentially a **two**-**stage** one. This is often justiﬁed, since the capacity planning decisions are strategic in nature and need to be decided over longer planning periods, while the assignment decisions are more at the operational level and can be decided when more information be- comes available. In principle, the model can be improved by considering the capacity decisions to be revised as time progresses and more information be- comes available. However, such a model would result in a multi-**stage** stochastic integer program which is almost impossible to solve with current computational technology. Furthermore, the **two**-**stage** model often can serve as a good enough approximation to the multi-**stage** problem.

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We investigate numerically the instability of three jets of the North Atlantic ocean (the Gulf- Stream, the North Atlantic current and the Azores current), and the vortices resulting from this instability. For this problem, we compare **two** hydrodynamical models (the shallow-water and the quasi-geostrophic equations) which we implement in identical conditions (**two**-layer stratification). First, both models are linearized and growth rates are calculated for zonal, normal-mode per- turbations on such jets. When we vary the Burger and the Rossby numbers of the jets and the wavenumber of the perturbations, the **two** linear models yield fairly similar results. Secondly, both **nonlinear** models (discretized on a fixed regular grid) are used to compute the finite-amplitude evolutions of the perturbed jets. These evolutions are qualitatively similar in both models, but the dynamical features (jet and vortices) are longer-lived in the shallow-water than in the quasi- geostrophic model. Also, only the former model exhibits an asymmetry between cyclones and anticyclones, which is physically explained.

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Abstract: Numerical Optimization algorithms presents the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. In this article, we propose some alternative iterative algorithms, with different order of convergence for minimization of non-linear functions. Then comparative study among the proposed algorithms and Newton’s **algorithm** is established by means of examples.

With the wide development of science and technology, the problem of solving **nonlinear** equations by numerical methods has gained more importance than before. In order to obtain efficient **algorithm** for the **nonlinear** equations which come from the practical problems, in this paper, we present and analyze **two** improved Newton-Raphson methods for solving **nonlinear** equations. The methods are free from second derivatives. Several numerical results illustrate the convergence behavior and computational efficiency of the proposed methods. Computational results demonstrate that they are more efficient and perform better than Newton-Raphson method and some existing methods.

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Ekezie et al (2013) in their research on paradox, a transportation problem with an objective function as the sum of a linear and linear fractional function was considered. The result of their analysis showed that a paradoxical situation arises in the sum of a linear and linear fractional transportation problem, when value of the objective function falls below the optimal value and this lower value was attainable by transporting larger number of passengers. An **algorithm** was discussed for finding initial basic feasible solution for the sum of a linear and linear fraction transportation problem and a sufficient condition for the existence of a paradoxical solution was established. Data collected from a secondary source were used for the explanation of the **algorithm**.

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Stochastic (mixed-) integer programs arise in a variety of situations in which discrete decisions combine with uncertainty in the data. Examples have been reported in the literature for some time, and include server location [28], batch sizing [21], electricity generation unit commitment [37], supply chain design [34], network interdiction [6, 15, 17], and many others [38]. The general combi- natorial, NP-hard nature of integer and mixed-integer problems makes them difficult to solve even when all the data are known, but special structure may allow for easier solution. A common approach to representing uncertainty in data is to formulate a finite number of discrete scenarios for the values of uncertain parameters together with associated probabilities. Methods for ob- taining scenarios do not concern us here, but often take the form of sampling from, or approximating, some stochastic process [9, 18, 30]. Decisions are classi- fied into **two** or more stages according to which parameter values are assumed to be known to the decision-maker when the decisions must be made. Those decisions that can be delayed until some parameter values are revealed are (1) modeled as scenario-dependent, (2) required to satisfy constraints using that scenario’s data, and (3) incur scenario-dependent costs. Implementability (or non-anticipativity) constraints are introduced to require that decisions not depend on data not yet revealed. When these model components are combined with an objective to minimize expected cost (where “cost” may include some measure of risk), the resulting extensive form of the stochastic program be- comes a very large mixed-integer program in which the underlying structure of the deterministic combinatorial problem has been obscured.

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The energy entering the resonant region of a system can be significantly reduced by introducing designed nonlinearities into the system. The basic choice of the nonlinearity can be either a **nonlinear** spring element or a **nonlinear** damping element. A numerical **algorithm** to compute and compare the energy reduction produced by these **two** types of designed elements is proposed in this study. Analytical results are used to demonstrate the procedure. The numerical results indicate that the designed **nonlinear** damping element produces low levels of energy at the higher order harmonics and no bifurcations in the system output response. In contrast the **nonlinear** spring based designs induce significant energy at the harmonics and can produce bifurcation behaviour. The conclusions provide an important basis for the design of **nonlinear** materials and **nonlinear** engineering systems.

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In this article, a method using the QRD-M **algorithm** [15,16], which uses QR decomposition (QRD) and the (M)-**algorithm** [17] to improve the demodulation eﬃ- ciency of PC/HC-MCM, is proposed and its performance is veriﬁed over an additive white Gaussian noise (AWGN) channel. This **algorithm** consists of **two** decoding stages. The ﬁrst decoding **stage** is responsible for a preliminary decision that serves to roughly ﬁnd candidate message data using the QRD-M **algorithm**. The second decod- ing **stage** is responsible for a ﬁnal decision that corrects the error contained in the candidate decoded at the ﬁrst decoding **stage**. Although another type of **two**-**stage** decoding **algorithm** has been considered [18], we have modiﬁed it to more eﬃciently and reliably decode the message data.

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Genetic Algorithms (GAs) are adaptive heuristic search **algorithm** premised on the evolutionary ideas of natural selection and genetic. The basic concept of GAs is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. As such they represent an intelligent exploitation of a random search within a defined search space to solve a problem [14].Genetic algorithms were formally introduced in the United States in the 1970s by John Holland at University of Michigan. The continuing price/performance improvements of computational systems have made them attractive for some types of optimization. In particular, genetic algorithms work very well on mixed (continuous and discrete), combinatorial problems. They are less susceptible to getting 'stuck' at local optima than gradient search methods [13][20]. Genetic algorithms has been widely studied, experimented and applied in many fields in engineering worlds. Not only does GAs provide an alternative method to solve problem, it consistently outperforms other traditional methods in most of the problems link. Many of the real world problems involved finding optimal parameters, which might prove difficult for traditional methods but ideal for GAs [7][8]. However, because of its outstanding performance in optimization, GAs has been wrongly regarded as a function optimizer [16]. Genetic **algorithm** is started with a set of solutions (represented by chromosomes) called population. Solutions from one population are taken and used to form a new population. This is motivated by a hope, that the new population will be better than the old one. Solutions which are selected to form new solutions (offspring) are selected according to their fitness - the more suitable they are the more chances they have to reproduce [21][22]. This is repeated until some condition (for example number of populations or improvement of the best solution) is satisfied. The genetic **algorithm** process consists of the following steps: Selection : Selecting **two** parent chromosomes.

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The cases where the interpolated quadratic has negative curvature and thus does not have a minimum must be treated in the practical implementation of this basic idea. To locate a group of points which implies a suitable quadratic model, the bracketing **algorithm** is often used. Another method is based on the repeated location of the minimum of a cubic polynomial fitted either to values of f at four or **two** points. Although the method is often fast, it also must avoid the search attracted to a maximum of the interpolating polynomial.

To solve unconstrained **nonlinear** minimization problems arising in the diversified field of engineering and technology, we have several methods to get solutions. For instance, multi-step **nonlinear** conjugate gradient methods [8], a scaled **nonlinear** conjugate gradient **algorithm**[2], a method called, ABS-MPVT **algorithm** [10] are used for solving unconstrained optimization problems. Newton’s method [11] is used for various classes of optimization problems, such as unconstrained minimization problems, equality constrained minimization problems. Chun[6] and Basto[3] have proposed and studied several methods for **nonlinear** equations with higher order convergence by using the decomposition technique of Adomian[1,13]. Vinay Kanwar et al. [18] introduced new **algorithm** called, external touch technique for solving the **nonlinear** equations. Further, they did the comparative study of the new algorithms and Newton’s **algorithm**. Jishe Feng [9] introduced **two** step iterative method for solving **nonlinear** equation with the comparative study of the new iterative method with Newton’s **Algorithm**, Abbasbandy method and Basto method. Changbum Chun [5] introduced sequence of iterative techniques improving Newton’s Method by the Decomposition Method for solving **nonlinear** equations. Recently, Rostam K.Saeed et. al. [12] presented a family of new iterative methods for solving **nonlinear** equations based on Newton’s method. Numerical examples are discussed to illustrate the efficiency of the methods and Behzad Ghanbari [4] introduced new general fourth–order family of methods for finding simple roots of **nonlinear** equations which is free from second derivative. J.F.Traub [15] introduced several iterative techniques for the solution of equations. C.Chun and Y. Ham[7] proposed some sixth order variants of Ostrowski root finding methods.

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This paper addresses the problem of control design and implementation for a **nonlinear** marine vessel manoeuvring model. The authors consider a highly **nonlinear** vessel 4 DOF model as the basis of this work. The control **algorithm** here proposed consists of a combination of **two** methodologies: i) an iteration technique that approximates the original **nonlinear** model by a sequence of linear time varying equations whose solution converge to the solution of the original **nonlinear** problem and, ii) a lead compensation design in which for each of the iterated linear time varying system generated, the controller is optimized at each time on the interval for better tracking performance. The control designed for the last iteration is then applied to the original **nonlinear** problem.

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In Chapter 4, we extend the cross-entropy methodology to the model defined in Miu and Ozdemir (2006). As opposed to the previous model we have studied, this par- ticular model exhibits correlation between the probability of default and the loss given default. To the best of our knowledge, IS has never been applied to this model although its correlation structure makes it a very interesting model to consider in practice. We show that applying a **two** **stage** IS estimator based on cross-entropy is very effective to reduce the variance. For the first **stage**, we can proceed as in the nor- mal copula scenario, however, the second **stage** becomes much more complicated. To sample from the IS distribution, we need to apply rejection sampling. By condition- ing appropriately, we can make this rejection sampling **algorithm** efficient (we found that in practice, the **algorithm** is on average twice as slow as crude Monte Carlo). The **algorithm** is fast and can be easily implemented, which makes it valuable for practitioners. The variance reduction obtained is also very impressive: the **algorithm** is capable of producing accurate estimations of probabilities up to 10 −37 .

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One important model which belongs to a family of linear generative models is in- dependent component analysis (ICA, see, e.g., Hyvärinen et al., 2001). This model is closely related to many models we have discussed. For instance, ICA formulated using the information-theoretic approach by Bell and Sejnowski (1995) is equiva- lent to the maximum likelihood solution of sparse coding (see Section 3.2.5) in the limit of no noise, when the numbers of inputs and sources are same (Olshausen and Field, 1997). Furthermore, by replacing the orthogonality constraint with the min- imal reconstruction regularization, it was shown by Le et al. (2011a) that a linear autoencoder (see Section 2.2.1) with a soft-sparsity regularization on hidden activa- tions is equivalent to ICA. Similarly, an approach that extracts principal components can be extended to extract independent components by employing certain **nonlinear** activation functions for the hidden units (see, e.g., Oja, 1997; Hyvärinen et al., 2001). ICA is further related to a restricted Boltzmann machine (see Section 4.4.2) via an energy-based model proposed by Teh et al. (2003).

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Abstract—We present an Altered Jacobian New- ton Iterative Method for solving **nonlinear** elliptic problems. Eﬀectiveness of the proposed method is demonstrated through numerical experiments. Com- parison of our method with Newton Iterative Method is also presented. Convergence of the Newton Itera- tive Method is highly sensitive to the initialization or initial guess. Reported numerical work shows the robustness of the Altered Jacobian Newton Iterative Method with respect to initialization.

control (?), particle swarm optimization (?), genetic algorithms (?), fuzzy logic methods (?),... etc. For most of these type of applications, **nonlinear** manoeuvring models in 1 degree of freedom (DOF) are considered, see ? or ? as example, still in these contributions, the coupling existing between the various variables is obviously not taken into account. Due to the complexity of some of the above cited **nonlinear** methods, the implementation may be tedious and time consuming from the computational point of view.

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