Search results for: Backward USSOR iterative matrix

Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Stability, Neural networks, Linear Matrix Inequalities (LMI) , Lyapunov function, Time-varying delays

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Authors: Long Jye Sheu, Horng-Shing Chiou, Wei Ching Chen

Abstract:

We propose a new perspective on speech communication using blind source separation. The original speech is mixed with key signals which consist of the mixing matrix, chaotic signals and a random noise. However, parts of the keys (the mixing matrix and the random noise) are not necessary in decryption. In practice implement, one can encrypt the speech by changing the noise signal every time. Hence, the present scheme obtains the advantages of a One Time Pad encryption while avoiding its drawbacks in key exchange. It is demonstrated that the proposed scheme is immune against traditional attacks.

Keywords: one time pad, blind source separation, independentcomponent analysis, speech encryption.

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Authors: Jing Li, Guang Zhou

Abstract:

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.

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Authors: Jianwei Wu

Abstract:

Based on the one-bit-matching principle and by turning the de-mixing matrix into an orthogonal matrix via certain normalization, Ma et al proposed a one-bit-matching learning algorithm on the Stiefel manifold for independent component analysis [8]. But this algorithm is not adaptive. In this paper, an algorithm which can extract kurtosis and its sign of each independent source component directly from observation data is firstly introduced.With the algorithm , the one-bit-matching learning algorithm is revised, so that it can make the blind separation on the Stiefel manifold implemented completely in the adaptive mode in the framework of natural gradient.

Keywords: Independent component analysis, kurtosis, Stiefel manifold, super-gaussians or sub-gaussians.

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Authors: Salim Ibrir

Abstract:

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

Keywords: Singular systems, Discrete-time systems, Regularization, LMIs

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Authors: K. Krishna Veni, S. Raja Balachandar

Abstract:

This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.

Keywords: 0-1 Multi constrained Knapsack problem, heuristic, computational complexity, NP-Hard problems.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: Xiguang Li

Abstract:

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

Keywords: Banach space, boundary value problem, differential equation, delay.

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Authors: Ahmad M. Sarhan, Omar I. Al Helalat

Abstract:

In this paper, an Arabic letter recognition system based on Artificial Neural Networks (ANNs) and statistical analysis for feature extraction is presented. The ANN is trained using the Least Mean Squares (LMS) algorithm. In the proposed system, each typed Arabic letter is represented by a matrix of binary numbers that are used as input to a simple feature extraction system whose output, in addition to the input matrix, are fed to an ANN. Simulation results are provided and show that the proposed system always produces a lower Mean Squared Error (MSE) and higher success rates than the current ANN solutions.

Keywords: ANN, Backpropagation, Gaussian, LMS, MSE, Neuron, standard deviation, Widrow-Hoff rule.

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Authors: Sergey Kopysov, Nikita Nedozhogin, Leonid Tonkov

Abstract:

The article presents a parallel iterative solver for large sparse linear systems which can be used on a heterogeneous platform. Traditionally, the problem of solving linear systems do not scale well on cluster containing multiple Central Processing Units (multi-CPUs cluster) or cluster containing multiple Graphics Processing Units (multi-GPUs cluster). For example, most of the attempts to implement the classical conjugate gradient method were at best counted in the same amount of time as the problem was enlarged. The paper proposes the pipelined variant of the conjugate gradient method (PCG), a formulation that is potentially better suited for hybrid CPU/GPU computing since it requires only one synchronization point per one iteration, instead of two for standard CG (Conjugate Gradient). The standard and pipelined CG methods need the vector entries generated by current GPU and other GPUs for matrix-vector product. So the communication between GPUs becomes a major performance bottleneck on miltiGPU cluster. The article presents an approach to minimize the communications between parallel parts of algorithms. Additionally, computation and communication can be overlapped to reduce the impact of data exchange. Using pipelined version of the CG method with one synchronization point, the possibility of asynchronous calculations and communications, load balancing between the CPU and GPU for solving the large linear systems allows for scalability. The algorithm is implemented with the combined use of technologies: MPI, OpenMP and CUDA. We show that almost optimum speed up on 8-CPU/2GPU may be reached (relatively to a one GPU execution). The parallelized solver achieves a speedup of up to 5.49 times on 16 NVIDIA Tesla GPUs, as compared to one GPU.

Keywords: Conjugate Gradient, GPU, parallel programming, pipelined algorithm.

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Authors: Pravin Gaikwad, Prakash Mahanwar

Abstract:

The main objective of incorporating natural fibers such as Henequen microfibers (NF) into the High Density Polyethylene (HDPE) polymer matrix is to reduce the cost and to enhance the mechanical as well as other properties. The Henequen microfibers were chopped manually to 5-7mm in length and added into the polymer matrix at the optimized concentration of 8 wt %. In order to facilitate the link between Henequen microfibers (NF) and HDPE matrix, coupling agent such as Glycidoxy (Epoxy) Functional Methoxy Silane (GPTS) at various concentrations from 0.1%, 0.3%, 0.5%, 0.7%, 0.9% and 1% by weight to the total fibers were added. The tensile strength of the composite increased marginally while % elongation at break of the composites decreased with increase in silane loading by wt %. Tensile modulus and stiffness observed increased at 0.9 wt % GPTS loading. Flexural as well as impact strength of the composite decreased with increase in GPTS loading by weight %. Dielectric strength of the composite also found increased marginally up to 0.5wt % silane loading and thereafter remained constant. 

Keywords: Henequen microfibers (NF), polymer composites, HDPE, coupling agent, GPTS

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Authors: Anesha Atul Shende

Abstract:

When we are aiming at high goals for economic development such as sustainable growth and development of economy, poverty reduction, and reduction in inequality etc., we must not forget to include each and everyone in the society in process of achieving these goals. This study particularly talks about women’s participation in economic activities with the special focus on the analysis of female labour force participation rate in the states of India. It makes comparison between the states having low female labour force participation with the states that have comparatively high female labour population. The study began with review of data on the current state of gender biases in employment. It has been found that the male workforce is dominant all across India. Further, the study highlights the major reasons for low women participation in economic activities in some of the backward Indian states like Bihar, etc. Reasons for low female participation are related to economic, cultural and social factors that are responsible for women’s unemployment. Afterwards, it analyses the reasons behind comparatively higher female participation in some of the other states in India. The case of the north-eastern region and state of Telangana and Tamil Nadu have been analysed in brief. These states show improvements in female labour force participation over a few decades. This is due to the government policies that have been adopted, women-friendly workplaces, availability of quality jobs for women etc. UN women has recognized the social and economic benefits of having an active female labour force in a country; if female unemployment declines, it will improve the growth rate of the nation as well as the welfare of the society. The study discusses the reasons why an economy must try to increase female workforce participation. It further provides suggestions to improve the conditions in backward states in India where the unemployment rate for women is high. The policy interventions and government schemes are some of the ways to recognise poor women workforce participation issues and work on it. The condition will improve when the changes would take place from regional level with social and moral support to the women.

Keywords: Women unemployment, labour force participation, women empowerment, economic growth and development, gender disparity.

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

Abstract:

We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: I. Davies, O. L. C. Haas

Abstract:

In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.

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Authors: Harald Rojacz, Markus Varga, Horst Winkelmann

Abstract:

Within this work High Temperature Single Impact Studies were performed to evaluate deformation mechanisms at different energy and momentum levels. To show the influence of different microstructures and hardness levels and their response to single impacts four different materials were tested at various temperatures up to 700°C. One carbide reinforced NiCrBSi based Metal Matrix Composite and three different steels were tested. The aim of this work is to determine critical energies for fracture appearance and the materials response at different energy and momenta levels. Critical impact loadings were examined at elevated temperatures to limit operating conditions in impact dominated regimes at elevated temperatures. The investigations on the mechanisms were performed using different means of microscopy at the surface and in metallographic cross sections. Results indicate temperature dependence of the occurrence of cracks in hardphase rich materials, such as Metal Matrix Composites High Speed Steels and the influence of different impact momenta at constant energies on the deformation of different steels.

Keywords: Deformation, High Temperature, Metal Matrix Composite, Single Impact Test, Steel.

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Authors: Hock Chuan, Lim

Abstract:

This paper presents an approach for identifying interactive effects using Network Science (NS) supported by Social Network Analysis (SNA) techniques. Based on general observations that learning processes and behaviors are shaped by the social relationships and influenced by learning environment, the central idea was to understand both the human and non-human interactive effects for a blended learning mode of delivery of computer science modules. Important findings include (a) the importance of non-human nodes to influence the centrality and transfer; (b) the degree of non-human and human connectivity impacts learning. This project reveals that the NS pattern and connectivity as measured by node relationships offer alternative approach for hypothesis generation and design of qualitative data collection. An iterative process further reinforces the analysis, whereas the experimental simulation option itself is an interesting alternative option, a hybrid combination of both experimental simulation and qualitative data collection presents itself as a promising and viable means to study complex scenario such as blended learning delivery mode. The primary value of this paper lies in the design of the approach for studying interactive effects of human (social nodes) and non-human (learning/study environment, Information and Communication Technologies (ICT) infrastructures nodes) components. In conclusion, this project adds to the understanding and the use of SNA to model and study interactive effects in blended social learning.

Keywords: Blended learning, network science, social learning, social network analysis, study environment.

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Authors: Zohreh O. Akbari

Abstract:

In this paper a deterministic polynomial-time algorithm is presented for the Clique problem. The case is considered as the problem of omitting the minimum number of vertices from the input graph so that none of the zeroes on the graph-s adjacency matrix (except the main diagonal entries) would remain on the adjacency matrix of the resulting subgraph. The existence of a deterministic polynomial-time algorithm for the Clique problem, as an NP-complete problem will prove the equality of P and NP complexity classes.

Keywords: Clique problem, Deterministic Polynomial-time Algorithm, Equality of P and NP Complexity Classes.

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Authors: I. Restrepo, S. Solorzano

Abstract:

This work was focused in to study the compatibility, dispersion and exfoliation of modified nanoclays in biodegradable polymers and evaluate its effect on the physical, mechanical and thermal properties on the biodegradable matrix used. The formulations have been developed with polylactic acid (PLA) and organically modified montmorillonite-type commercial nanoclays (Cloisite 15, Cloisite 20, and Cloisite 30B) in the presence of a plasticizer agent, specifically Polyethylene Glycol of low molecular weight. Different compositions were evaluated, in order to identify the influence of each nanoclayin the polymeric matrix. The mixtures were characterized by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), X-ray diffraction (DRX), transmission electron microscopy (TEM) and Tensile Test. These tests have allowed understanding the behavior of each of the mixtures developed.

Keywords: Biopolymers, Nanoclays, polylacticacid (PLA), polymer blends.

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Authors: Manouchehr Amiri

Abstract:

This article presents a general notion of physical bit information that is compatible with the basics of quantum mechanics and incorporates the Shannon entropy as a special case. This notion of physical information leads to the Binary Data Matrix model (BDM), which predicts the basic results of quantum mechanics, general relativity, and black hole thermodynamics. The compatibility of the model with holographic, information conservation, and Landauer’s principle is investigated. After deriving the “Bit Information principle” as a consequence of BDM, the fundamental equations of Planck, De Broglie, Bekenstein, and mass-energy equivalence are derived.

Keywords: Physical theory of information, binary data matrix model, Shannon information theory, bit information principle.

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Authors: Hazem M. El-Bakry, Qiangfu Zhao

Abstract:

In recent years, fast neural networks for object/face detection have been introduced based on cross correlation in the frequency domain between the input matrix and the hidden weights of neural networks. In our previous papers [3,4], fast neural networks for certain code detection was introduced. It was proved in [10] that for fast neural networks to give the same correct results as conventional neural networks, both the weights of neural networks and the input matrix must be symmetric. This condition made those fast neural networks slower than conventional neural networks. Another symmetric form for the input matrix was introduced in [1-9] to speed up the operation of these fast neural networks. Here, corrections for the cross correlation equations (given in [13,15,16]) to compensate for the symmetry condition are presented. After these corrections, it is proved mathematically that the number of computation steps required for fast neural networks is less than that needed by classical neural networks. Furthermore, there is no need for converting the input data into symmetric form. Moreover, such new idea is applied to increase the speed of neural networks in case of processing complex values. Simulation results after these corrections using MATLAB confirm the theoretical computations.

Keywords: Fast Code/Data Detection, Neural Networks, Cross Correlation, real/complex values.

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Authors: N. Feroze, M. Aslam

Abstract:

The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.

Keywords: Fisher information matrix, confidence intervals, censoring.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

Abstract:

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: Mohammed T. Hayajneh, Adel Mahmood Hassan, Moath AL-Qudah

Abstract:

Burnishing is increasingly used as a finishing operation to improve surface roughness and surface hardness. This can be achieved by applying a hard ball or roller onto metallic surfaces under pressure, in order to achieve many advantages in the metallic surface. In the present work, the feed rate, speed and force have been considered as the basic burnishing parameters to study the surface roughness and surface hardness of metallic matrix composites. The considered metal matrix composites were made from Aluminum-Magnesium-Graphite with five different weight percentage of graphite. Both effects of burnishing parameters mentioned above and the graphite percentage on the surface hardness and surface roughness of the metallic matrix composites were studied. The results of this investigation showed that the surface hardness of the metallic composites increases with the increase of the burnishing force and decreases with the increase in the burnishing feed rate and burnishing speed. The surface roughness of the metallic composites decreases with the increasing of the burnishing force, feed rate, and speed to certain values, then it starts to increase. On the other hand, the increase in the weight percentage of the graphite in the considered composites causes a decrease in the surface hardness and an increase in the surface roughness.

Keywords: Burnishing process, Al-Mg-Graphite composites, Surface hardness, Surface roughness.

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Authors: Jiann-Ming Wu, Hsiao-Chang Chen, Chun-Chang Wu, Pei-Hsun Hsu

Abstract:

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

Keywords: Blind image deconvolution, linear shift-invariant(LSI), linear image degradation model, radial basis functions (rbf), recursive function, annealed Hopfield neural networks.

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Authors: S. Umarani, D. Sharmila

Abstract:

A Distributed Denial of Service (DDoS) attack is a major threat to cyber security. It originates from the network layer or the application layer of compromised/attacker systems which are connected to the network. The impact of this attack ranges from the simple inconvenience to use a particular service to causing major failures at the targeted server. When there is heavy traffic flow to a target server, it is necessary to classify the legitimate access and attacks. In this paper, a novel method is proposed to detect DDoS attacks from the traces of traffic flow. An access matrix is created from the traces. As the access matrix is multi dimensional, Principle Component Analysis (PCA) is used to reduce the attributes used for detection. Two classifiers Naive Bayes and K-Nearest neighborhood are used to classify the traffic as normal or abnormal. The performance of the classifier with PCA selected attributes and actual attributes of access matrix is compared by the detection rate and False Positive Rate (FPR).

Keywords: Distributed Denial of Service (DDoS) attack, Application layer DDoS, DDoS Detection, K- Nearest neighborhood classifier, Naive Bayes Classifier, Principle Component Analysis.

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Authors: Tamal Bose, Zhurun Zhang, Miloje Radenkovic, Ojas Chauhan

Abstract:

In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A “structuretransformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.

Keywords: Digital filters, minimum noise, multiplier-free, quantization, state-space.

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

Abstract:

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: Chaos theory, GMM estimator, Lyapunov Exponent, Monetary System, Taylor Rule.

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Authors: P. Chultheera, T. Rirksomboon, S. Kulprathipanja, C. Liu, W. Chinsirikul, N. Kerddonfag

Abstract:

Gas separation by selective transport through polymeric membranes is one of the rapid growing branches of membrane technology. However, the tradeoff between the permeability and selectivity is one of the critical challenges encountered by pure polymer membranes, which in turn limits their large-scale application. To enhance gas separation performances, mixed matrix membranes (MMMs) have been developed. In this study, MMMs were prepared by a solution-coating method and tested for CO₂/CH₄ separation through permeability and selectivity using a membrane testing unit at room temperature and a pressure of 100 psig. The fabricated MMMs were composed of silicone rubber dispersed with the activated carbon individually absorbed with polyethylene glycol (PEG) as a liquid additive. PEG emulsified silicone rubber MMMs showed superior gas separation on cellulose acetate membrane with both high permeability and selectivity compared with silicone rubber membrane and alone support membrane. However, the MMMs performed limited stability resulting from the undesirable PEG leakage. To stabilize the MMMs, PEG was then incorporated into activated carbon by adsorption. It was found that the incorporation of solid and liquid was effective to improve the separation performance of MMMs.

Keywords: Mixed matrix membrane, membrane, CO2/CH4 separation, activated carbon.

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