Feature Selection Using Grey Wolf Optimization with Random Differential Grouping

Big data are regarded as a tremendous technology for processing a huge variety of data in a short time and with a large storage capacity.The user’s access over the internet creates massive data processing over the internet.Big data require an intelligent feature selection model by addressing huge varieties of data.Traditional feature selection techniques are only applicable to simple data mining.Intelligent techniques are needed in big data processing and machine learning for an efficient classification.Major feature selection algorithms read the input features as they are.Then,the features are preprocessed and classified.Here,an algorithm does not consider the relatedness.During feature selection,all features are misread as outputs.Accordingly,a less optimal solution is achieved.In our proposed research,we focus on the feature selection by using supervised learning techniques called grey wolf optimization(GWO)with decomposed random differential grouping(DrnDG-GWO).First,decomposition of features into subsets based on relatedness in variables is performed.Random differential grouping is performed using a fitness value of two variables.Now,every subset is regarded as a population in GWO techniques.The combination of supervised machine learning with swarm intelligence techniques produces best feature optimization results in this research.Once the features are optimized,we classify using advanced kNN process for accurate data classification.The result of DrnDGGWO is compared with those of the standard GWO and GWO with PSO for feature selection to compare the efficiency of the proposed algorithm.The accuracy and time complexity of the proposed algorithm are 98%and 5 s,which are better than the existing techniques.

Finite Difference Scheme for Solving Parabolic Partial Differential Equations with Random Variable Input under Mean Square Sense

This study deal with seven points finite difference method to find the approximation solutions in the area of mean square calculus solutions for linear random parabolic partial differential equations. Several numerical examples are presented to show the ability and efficiency of this method.

Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method

The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

GAUSS WHITE NOISE PERTURBATIONS OF NONHOLONOMIC MECHANICAL SYSTEMS

The perturbations of nonholonomic mechanical systems under the Gauss white noises are studied in this paper. It is proved that the differential equations of the first-order moments of the solution process coincide with the corresponding equations in the non-perturbational case, and that there are e2 -terms but no e-terms in the differential equations of the second-order moments. Two propositions are obtained. Finally, an example is given to illustrate the application of the results.

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.

Some Notes of p-Moment Boundedness of Nonlinear Differential Equation with Pandom Impulses

A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.

Existence and Uniqueness of Solutions to Random Impulsive Differential Systems

The existence and uniqueness in mean square of solutions to certain random impulsive differential systems is discussed in this paper. Cauchy-Schwarz inequality, Lipschtiz condition and techniques in stochastic analysis are employed in achieve the desired results.

Quasimonotone random and stochastic functional differential equations with applications

In this paper, we study monotone properties of random and stochastic functional differential equations and their global dynamics. First, we show that random functional differential equations(RFDEs)generate the random dynamical system(RDS) if and only if all the solutions are globally defined, and establish the comparison theorem for RFDEs and the random Riesz representation theorem. These three results lead to the Borel measurability of coefficient functions in the Riesz representation of variational equations for quasimonotone RFDEs, which paves the way following the Smith line to establish eventual strong monotonicity for the RDS under cooperative and irreducible conditions. Then strong comparison principles, strong sublinearity theorems and the existence of random attractors for RFDEs are proved. Finally, criteria are presented for the existence of a unique random equilibrium and its global stability in the universe of all the tempered random closed sets of the positive cone. Applications to typical random or stochastic delay models in monotone dynamical systems,such as biochemical control circuits, cyclic gene models and Hopfield-type neural networks, are given.

On Existence and Uniqueness of Random Impulsive Differential Equations

This paper studies existence and uniqueness for random impulsive differential equations.The authors first generalize a random fixed point theorem of Schaefer's type.Then the authors shall rely on the generalized Schaefer's type random fixed point theorem to discuss the existence of the system.In addition,the authors study the existence and uniqueness of random impulsive differential equations by applying random Banach fixed point theorem and obtain some less conservative results.Finally,an example is given to illustrate the effectiveness of the results.

Computing Nonlinear LTS Estimator Based on a Random Differential Evolution Strategy

Nonlinear least trimmed squares （NLTS） estimator is a very important kind of nonlinear robust estimator, which is widely used for recovering an ideal high-quality signal from contaminated data. However, the NLTS estimator has not been widely used because it is hard to compute, This paper develops an algorithm to compute the NLTS estimator based on a random differential evolution （DE） strategy. The strategy which uses random DE schemes and control variables improves the DE performance. The simulation results demonstrate that the algorithm gives better performance and is more convenient than existing computing algorithms for the NLTS estimator. The algorithm makes the NLTS estimator easy to apply in practice, even for large data sets, e.g. in a data mining context.

Efficient Collocational Approach for Parametric Uncertainty Analysis

A numerical algorithm for effective incorporation of parametric uncertainty into mathematical models is presented.The uncertain parameters are modeled as random variables,and the governing equations are treated as stochastic.The solutions,or quantities of interests,are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters.A high-order stochastic collocation method is employed to solve the solution statistics,and more importantly,to reconstruct the polynomial expansion.While retaining the high accuracy by polynomial expansion,the resulting“pseudo-spectral”type algorithm is straightforward to implement as it requires only repetitive deterministic simulations.An estimate on error bounded is presented,along with numerical examples for problems with relatively complicated forms of governing equations.

Design of power balance SRAM for DPA-resistance

A power balance static random-access memory（SRAM） for resistance to differential power analysis（DPA） is proposed. In the proposed design, the switch power consumption and short-circuit power consumption are balanced by discharging and pre-charging the key nodes of the output circuit and adding an additional shortcircuit current path. Thus, the power consumption is constant in every read cycle. As a result, the DPA-resistant ability of the SRAM is improved. In 65 nm CMOS technology, the power balance SRAM is fully custom designed with a layout area of 5863.6 μm^2.The post-simulation results show that the normalized energy deviation（NED） and normalized standard deviation（NSD） are 0.099% and 0.04%, respectively. Compared to existing power balance circuits, the power balance ability of the proposed SRAM has improved 53%.