The analysis of the number of fixed points in the key extending algorithm of RC4

The probabilities of the state transitions of the initial value S 0 in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.

Extended Deep Learning Algorithm for Improved Brain Tumor Diagnosis System

At present,the prediction of brain tumors is performed using Machine Learning(ML)and Deep Learning(DL)algorithms.Although various ML and DL algorithms are adapted to predict brain tumors to some range,some concerns still need enhancement,particularly accuracy,sensitivity,false positive and false negative,to improve the brain tumor prediction system symmetrically.Therefore,this work proposed an Extended Deep Learning Algorithm(EDLA)to measure performance parameters such as accuracy,sensitivity,and false positive and false negative rates.In addition,these iterated measures were analyzed by comparing the EDLA method with the Convolutional Neural Network(CNN)way further using the SPSS tool,and respective graphical illustrations were shown.The results were that the mean performance measures for the proposed EDLA algorithm were calculated,and those measured were accuracy(97.665%),sensitivity(97.939%),false positive(3.012%),and false negative(3.182%)for ten iterations.Whereas in the case of the CNN,the algorithm means accuracy gained was 94.287%,mean sensitivity 95.612%,mean false positive 5.328%,and mean false negative 4.756%.These results show that the proposed EDLA method has outperformed existing algorithms,including CNN,and ensures symmetrically improved parameters.Thus EDLA algorithm introduces novelty concerning its performance and particular activation function.This proposed method will be utilized effectively in brain tumor detection in a precise and accurate manner.This algorithm would apply to brain tumor diagnosis and be involved in various medical diagnoses aftermodification.If the quantity of dataset records is enormous,then themethod’s computation power has to be updated.

An Extended Algorithm of Flexibility Analysis in Chemical Engineering Processes

An extended algorithm of flexibility analysis with a local adjusting method for flexibility region of chemical processes, which is based on the active constraint strategy, is proposed, which fully exploits the flexibility region of the process system operation. The hyperrectangular flexibility region determined by the extended algorithm is larger than that calculated by the previous algorithms. The limitation of the proposed algorithm due to imperfect convexity and its corresponding verification measure are also discussed. Both numerical and actual chemical process examples are presented to demonstrate the effectiveness of the new algorithm.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

An extended particle swarm optimization algorithm based on coarse-grained and fine-grained criteria and its application

In order to study the problem that particle swarm optimization (PSO) algorithm can easily trap into local mechanism when analyzing the high dimensional complex optimization problems, the optimization calculation using the information in the iterative process of more particles was analyzed and the optimal system of particle swarm algorithm was improved. The extended particle swarm optimization algorithm (EPSO) was proposed. The coarse-grained and fine-grained criteria that can control the selection were given to ensure the convergence of the algorithm. The two criteria considered the parameter selection mechanism under the situation of random probability. By adopting MATLAB7.1, the extended particle swarm optimization algorithm was demonstrated in the resource leveling of power project scheduling. EPSO was compared with genetic algorithm (GA) and common PSO, the result indicates that the variance of the objective function of resource leveling is decreased by 7.9%, 18.2%, respectively, certifying the effectiveness and stronger global convergence ability of the EPSO.

Solution of Algebraic Lyapunov Equation on Positive-Definite Hermitian Matrices by Using Extended Hamiltonian Algorithm

This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance between􀀀AHX􀀀XA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

Full Euclidean Algorithm by Means of a Steady Walk

Let x and y be two positive real numbers with x < y. Consider a traveler, on the interval [0, y/2], departing from 0 and taking steps of length equal to x. Every time a step reaches an endpoint of the interval, the traveler rebounds off the endpoint in order to complete the step length. We show that the footprints of the traveler are the output of a full Euclidean algorithm for x and y, whenever y/x is a rational number. In the case that y/x is irrational, the algorithm is, theoretically, not finite;however, it is a new tool for the study of its irrationality.

Extended Active Contour Algorithm Based on Color Variance

General active contour algorithm, which uses the intensity of the image, has been used to actively segment objects. Because the objects have a similar intensity but different colors, it is difficult to segment any object from the others, Moreover, this algodthm can only be used in the simple environment since it is very sensitive to noise. In tinter to solve these problems. This paper proposes an extended active contour algorithm based on a color variance. In complex images, the color variance energy as the image energy is introduced into the general active contour algorithm. Experimental results show that the proposed active contour algorithm is very effective in various environments.

A Regularized Randomized Kaczmarz Algorithm for Large Discrete Ill-Posed Problems

Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.

A Numerical Study of the TipWake of aWind Turbine Impeller Using Extended Proper Orthogonal Decomposition

The behavior of the tip wake of a wind turbine is one of the hot issues in the wind power field.This problem can partially be tackled using Computational Fluid Dynamics(CFD).However,this approach lacks the ability to provide insights into the spatial structure of important high-order flows.Therefore,with the horizontal axis wind turbine as the main focus,in this work,firstly,we conduct CFD simulations of the wind turbine in order to obtain a data-driven basis relating to multiple working conditions for further analysis.Then,these data are studied using an extended Proper Orthogonal Decomposition(POD)algorithm.The quantitative results indicate that the tip vortex in the wake has a complicated spatio-temporal morphological configuration in the higher-order extended POD space.The radial velocity modes obtained are effective and credible,and such reconstructed flow of the tip vortex becomes clearer with the increase of the reconstruction orders.Interestingly,the changes of relatively high-order correlation coefficients are essentially affected by the periodic fusion of tip and central eddies in the wake.

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (II)

When using H_∞ techniques to design decentralized controllers for large systems, the whole system is divided into subsystems, which are analysed using H_∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H_∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H_∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick_Williams algorithm were transplanted from structural mechanics to compute the optimal H_∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H_∞ control are presented in part (Ⅰ) of the paper. The modal synthesis method for computation of the optimal H_∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).

Discriminant Genetic Algorithm Extended (DGAE) model for seasonal sand and dust storm prediction

Here we use a Discriminant Genetic Algorithm Extended (DGAE) model to diagnose and predict seasonal sand and dust storm (SDS) activities occurring in Northeast Asia. The study employed the regular meteorological data, including surface data, upper air data, and NCEP reanalysis data, collected from 1980–2006. The regional, seasonal, and annual differences of 3-D atmospheric circulation structures and SDS activities in the context of spatial and temporal distributions were given. Genetic algorithms were introduced with the further extension of promoting SDS seasonal predication from multi-level resolution. Genetic probability was used as a substitute for posterior probability of multi-level discriminants, to show the dual characteristics of crossover inheritance and mutation and to build a non-linear adaptability function in line with extended genetic algorithms. This has unveiled the spatial distribution of the maximum adaptability, allowing the forecast field to be defined by the population with the largest probability, and made discriminant genetic extension possible. In addition, the effort has led to the establishment of a regional model for predicting seasonal SDS activities in East Asia. The model was tested to predict the spring SDS activities occurring in North China from 2007 to 2009. The experimental forecast resulted in highly discriminant intensity ratings and regional distributions of SDS activities, which are a meaningful reference for seasonal SDS predictions in the future.

Stability analysis of the extended ADI-FDTD technique including lumped models

The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, capacitor, and inductor, and three different formulations for each model are analyzed： the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.

A PRECISE METHOD FOR SOLVING WAVE PROPAGATION IN HOLLOW SANDWICH CYLINDERS WITH PRISMATIC CORES

Wave propagation in infinitely long hollow sandwich cylinders with prismatic cores is analyzed by the extended Wittriek-Williams （W-W） algorithm and the precise integration method （PIM）. The effective elastic constants of prismatic cellular materials are obtained by the homogenization method. By applying the variational principle and introducing the dual variables the canonical equations of Hamiltonian system are constructed. Thereafter, the wave propagation problem is converted to an eigenvalue problem. In numerical examples, the effects of the prismatic cellular topology, the relative density, and the boundary conditions on dispersion relations, respectively, are investigated.

Low complexity NB-LDPC decoder based on shared comparator architecture for ECN/EVN

Non-binary low density parity check （NB-LDPC） codes are considered as preferred candidate in conditions where short/medium codeword length codes and better performance at low signal to noise ratios （SNR） are required. They have better burst error correcting performance, especially with high order Galois fields （GF）. A shared comparator （SCOMP） architecture for elementary of check node （ECN）/elementary of variable node （EVN） to reduce decoder complexity is introduced because high complexity of check node （CN） and variable node （VN） prevent NB-LDPC decoder from widely applications. The decoder over GF（16） is based on the extended rain-sum （EMS） algorithm. The decoder matrix is an irregular structure as it can provide better performance than regular ones. In order to provide higher throughput and increase the parallel processing efficiency, the clock which is 8 times of the system frequency is adopted in this paper to drive the CN/VN modules. The decoder complexity can be reduced by 28% from traditional decoder when SCOMP architecture is introduced. The result of synthesis software shows that the throughput can achieve 34 Mbit/s at 10 iterations. The proposed architecture can be conveniently extended to GF such as GF（64） or GF（256）. Compared with previous works, the decoder proposed in this paper has better hardware efficiency for practical applications.