Search results for: NFV (Network Functions Virtualization)

Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Emad Amar, Tawfik Khattab, Fatma Zada

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Predicting earthquakes is an important issue in the study of geography. Accurate prediction of earthquakes can help people to take effective measures to minimize the loss of personal and economic damage, such as large casualties, destruction of buildings and broken of traffic, occurred within a few seconds. United States Geological Survey (USGS) science organization provides reliable scientific information of Earthquake Existed throughout history & Preliminary database from the National Center Earthquake Information (NEIC) show some useful factors to predict an earthquake in a seismic area like Aleutian Arc in the U.S. state of Alaska. The main advantage of this prediction method that it does not require any assumption, it makes prediction according to the future evolution of object's time series. The article compares between simulation data result from trained BP and RBF neural network versus actual output result from the system calculations. Therefore, this article focuses on analysis of data relating to real earthquakes. Evaluation results show better accuracy and higher speed by using radial basis functions (RBF) neural network.

Keywords: BP neural network, prediction, RBF neural network, earthquake

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Authors: M. Khouil, N. Saber, M. Mestari

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This study aimed to propose, a different architecture of a Path Planning using the NECMOP. where several nonlinear objective functions must be optimized in a conflicting situation. The ability to detect and avoid collision is very important for mobile intelligent machines. However, many artificial vision systems are not yet able to quickly and cheaply extract the wealth information. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons linear and threshold logic, which simplified the actual implementation of all the networks proposed. This article represents a comprehensive algorithm that determine through the AMAXNET network a measure (a mini-maximum point) in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: path planning, collision detection, convex polyhedron, neural network

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Thomas Adi Purnomo Sidhi

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Nowadays, network is an essential need in almost every part of human daily activities. People now can seamlessly connect to others through the Internet. With advanced technology, our personal data now can be more easily accessed. One of many components we are concerned for delivering the best network is a security issue. This paper is proposing a method that provides more options for security. This research aims to improve network security by focusing on the physical layer which is the first layer of the OSI model. The layer consists of the basic networking hardware transmission technologies of a network. With the use of observation method, the research produces a schematic design for enhancing the network security through the gray code converter.

Keywords: network, network security, grey code, physical layer

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Authors: Elabed Saud

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This paper introduces the new ability of Artificial Neural Networks (ANNs) in estimating speed and controlling the separately excited DC motor. The neural control scheme consists of two parts. One is the neural estimator which is used to estimate the motor speed. The other is the neural controller which is used to generate a control signal for a converter. These two neutrals are training by Levenberg-Marquardt back-propagation algorithm. ANNs are the standard three layers feed-forward neural network with sigmoid activation functions in the input and hidden layers and purelin in the output layer. Simulation results are presented to demonstrate the effectiveness of this neural and advantage of the control system DC motor with ANNs in comparison with the conventional scheme without ANNs.

Keywords: Artificial Neural Network (ANNs), excited DC motor, convenional controller, speed Controller

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Authors: Chia-Feng Lu, Yuh-Jen Wang, Yu-Te Wu, Sui-Hing Yan

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This study aimed at investigating whether the functional brain networks constructed using the initial EEG (obtained when patients first visited hospital) can be correlated with the progression of cognitive decline calculated as the changes of mini-mental state examination (MMSE) scores between the latest and initial examinations. We integrated the time–frequency cross mutual information (TFCMI) method to estimate the EEG functional connectivity between cortical regions, and the network analysis based on graph theory to investigate the organization of functional networks in aMCI. Our finding suggested that higher integrated functional network with sufficient connection strengths, dense connection between local regions, and high network efficiency in processing information at the initial stage may result in a better prognosis of the subsequent cognitive functions for aMCI. In conclusion, the functional connectivity can be a useful biomarker to assist in prediction of cognitive declines in aMCI.

Keywords: cognitive decline, functional connectivity, MCI, MMSE

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Kassim A. Jassim

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In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

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Authors: Nihed Bahria El Asghar, Imen Jouili, Mounir Frikha

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Inter-datacenter transport network is very bandwidth and delay demanding. The data transferred over such a network is also highly QoS-exigent mostly because a huge volume of data should be transported transparently with regard to the application user. To avoid the data transfer failure, a backup path should be reserved. No re-routing delay should be observed. A dedicated 1+1 protection is however not applicable in inter-datacenter transport network because of the huge spare capacity. In this context, we propose a survivable virtual network with minimal backup based on network coding (1 ⊕ 1) and solve it using a modified Dijkstra-based heuristic.

Keywords: network coding, dedicated protection, spare capacity, inter-datacenters transport network

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Artion Kashuri, Rozana Liko

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In this paper, the authors establish an integral identity using delta differentiable functions. By applying this identity, some new results via a general class of convex functions with respect to two nonnegative functions on a time scale are given. Also, for suitable choices of nonnegative functions, some special cases are deduced. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtained as well. We hope that current work using our idea and technique will attract the attention of researchers working in mathematical analysis, mathematical inequalities, numerical analysis, special functions, fractional calculus, quantum mechanics, quantum calculus, physics, probability and statistics, differential and difference equations, optimization theory, and other related fields in pure and applied sciences.

Keywords: convex functions, Hermite-Hadamard inequality, special means, time scale

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Authors: Ameen Jameel Alawneh

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A Mobile ad-hoc network (MANET) is a collection of wireless mobile hosts that dynamically form a temporary network without the aid of a system administrator. It has neither fixed infrastructure nor wireless ad hoc sessions. It inherently reaches several nodes with a single transmission, and each node functions as both a host and a router. The network maybe represented as a set of clusters each managed by clusterhead. The cluster size is not fixed and it depends on the movement of nodes. We proposed a clusterhead size algorithm (CHSize). This clustering algorithm can be used by several routing algorithms for ad hoc networks. An elected clusterhead is assigned for communication with all other clusters. Analysis and simulation of the algorithm has been implemented using GloMoSim networks simulator, MATLAB and MAPL11 proved that the proposed algorithm achieves the goals.

Keywords: simulation, MANET, Ad-hoc, cluster head size, linked cluster algorithm, loss and dropped packets

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Fariha Asif

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The main purpose of this study was to investigate the effectiveness of eclectic approach in teaching of communicative functions. The objectives of the study were to get the information about the use of communicative functions through eclectic approach and to point out the most effective way of teaching functional communication and social interaction with the help of communicative activities through eclectic approach. The next step was to select sample from the selected population. As the research was descriptive so a questionnaire was developed on the basis of hypothesis and distributed to different selected schools of Lahore, Pakistan. Then data was tabulated, analyzed and interpreted through computer by finding percentages of different responses given by teachers to see the results. It was concluded that eclectic approach is effective in teaching communicative functions and communicative functions are better when taught through eclectic approach and communicative activities are more appropriate way of teaching communicative functions. It was found those teachers who were qualified in ELT gave better opinions as compare to those who did not have this degree. Techniques like presentations, dialogues and roleplay proved to be effective for teaching functional communication through communicative activities and also motivate the students not only in learning rules but also in using them to communicate with others.

Keywords: methodology, functions, teaching, ESP

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Authors: Takumi Shindo, Koji Okamura

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The first generation of the wide area network was circuit centric network. How the optimal circuit can be signed was the most important issue to get the best performance. This architecture had succeeded for line based telephone system. The second generation was host centric network and Internet based on this architecture has very succeeded world widely. And Internet became as new social infrastructure. Currently the architecture of the network is based on the location of the information. This future network is called Information centric network (ICN). The information-centric network (ICN) has being researched by many projects and different architectures for implementation of ICN have been proposed. The goal of this study is to compare performances of those ICN architectures. In this paper, the authors propose general ICN model which can represent two typical ICN architectures and compare communication performances using request routing. Finally, simulation results are shown. Also, we assume that this network architecture should be adapt to energy on-demand routing.

Keywords: ICN, information centric network, CCN, energy

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Arthur D. Wiedemann, Christopher Fuller, Kyle A. Pascioni

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With the introduction of electric motors, small unmanned aerial vehicle designers have to consider trade-offs between acoustic noise and thrust generated. Currently, there are few low-computational tools available for predicting acoustic noise emitted by a propeller into the far-field. Artificial neural networks offer a highly non-linear and adaptive model for predicting isolated and interactive tonal noise. But neural networks require large data sets, exceeding practical considerations in modeling experimental results. A methodology known as physics guided machine learning has been applied in this study to reduce the required data set to train the network. After building and evaluating several neural networks, the best model is investigated to determine how the network successfully predicts the acoustic waveform. Lastly, a post-network transfer function is developed to remove discontinuity from the predicted waveform. Overall, methodologies from physics guided machine learning show a notable improvement in prediction performance, but additional loss functions are necessary for constructing predictive networks on small datasets.

Keywords: aeroacoustics, machine learning, propeller, rotor, neural network, physics guided machine learning

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Authors: Mohammad Arif Khan

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This paper analyzes and presents the development of Artificial Neural Network based controller of space vector modulation (ANN-SVPWM) for a seven-phase voltage source inverter. At first, the conventional method of producing sinusoidal output voltage by utilizing six active and one zero space vectors are used to synthesize the input reference, is elaborated and then new PWM scheme called Artificial Neural Network Based PWM is presented. The ANN based controller has the advantage of the very fast implementation and analyzing the algorithms and avoids the direct computation of trigonometric and non-linear functions. The ANN controller uses the individual training strategy with the fixed weight and supervised models. A computer simulation program has been developed using Matlab/Simulink together with the neural network toolbox for training the ANN-controller. A comparison of the proposed scheme with the conventional scheme is presented based on various performance indices. Extensive Simulation results are provided to validate the findings.

Keywords: space vector PWM, total harmonic distortion, seven-phase, voltage source inverter, multi-phase, artificial neural network

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Authors: Tanmay Raj, Vedika Gupta

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For its groundbreaking and substantial power, cloud computing is today’s most popular breakthrough. It is a sort of Internet-based computing that allows users to request and receive numerous services in a cost-effective manner. Virtualization, grid computing, and utility computing are the most widely employed emerging technologies in cloud computing, making it the most powerful. However, cloud computing still has a number of key challenges, such as security, load balancing, and non-critical failure adaption, to name a few. The massive growth of cloud computing will put an undue strain on servers. As a result, network performance will deteriorate. A good load balancing adjustment can make cloud computing more productive and in- crease client fulfillment execution. Load balancing is an important part of cloud computing because it prevents certain nodes from being overwhelmed while others are idle or have little work to perform. Response time, cost, throughput, performance, and resource usage are all parameters that may be improved using load balancing.

Keywords: cloud computing, load balancing, computing, SIP server clusters

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Authors: Dylan Santos De Pinho, Nabil Ouerhani

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Energy consumption of machine-tools is becoming critical for machine-tool builders and end-users because of economic, ecological and legislation-related reasons. Many machine-tool builders are seeking for solutions that allow the reduction of energy consumption of machine-tools while preserving the same productivity rate and the same quality of machined parts. In this paper, we present the first results of a project conducted jointly by academic and industrial partners to reduce the energy consumption of a Swiss-Type lathe. We employ genetic algorithms to find optimal machining parameters – the set of parameters that lead to the best trade-off between energy consumption, part quality and tool lifetime. Three main machining process parameters are considered in our optimization technique, namely depth of cut, spindle rotation speed and material feed rate. These machining process parameters have been identified as the most influential ones in the configuration of the Swiss-type machining process. A state-of-the-art multi-objective genetic algorithm has been used. The algorithm combines three fitness functions, which are objective functions that permit to evaluate a set of parameters against the three objectives: energy consumption, quality of the machined parts, and tool lifetime. In this paper, we focus on the investigation of the fitness function related to energy consumption. Four different energy consumption related fitness functions have been investigated and compared. The first fitness function refers to the Kienzle cutting force model. The second fitness function uses the Material Removal Rate (RMM) as an indicator of energy consumption. The two other fitness functions are non-deterministic, learning-based functions. One fitness function uses a simple Neural Network to learn the relation between the process parameters and the energy consumption from experimental data. Another fitness function uses Lasso regression to determine the same relation. The goal is, then, to find out which fitness functions predict best the energy consumption of a Swiss-Type machining process for the given set of machining process parameters. Once determined, these functions may be used for optimization purposes – determine the optimal machining process parameters leading to minimum energy consumption. The performance of the four fitness functions has been evaluated. The Tornos DT13 Swiss-Type Lathe has been used to carry out the experiments. A mechanical part including various Swiss-Type machining operations has been selected for the experiments. The evaluation process starts with generating a set of CNC (Computer Numerical Control) programs for machining the part at hand. Each CNC program considers a different set of machining process parameters. During the machining process, the power consumption of the spindle is measured. All collected data are assigned to the appropriate CNC program and thus to the set of machining process parameters. The evaluation approach consists in calculating the correlation between the normalized measured power consumption and the normalized power consumption prediction for each of the four fitness functions. The evaluation shows that the Lasso and Neural Network fitness functions have the highest correlation coefficient with 97%. The fitness function “Material Removal Rate” (MRR) has a correlation coefficient of 90%, whereas the Kienzle-based fitness function has a correlation coefficient of 80%.

Keywords: adaptive machining, genetic algorithms, smart manufacturing, parameters optimization

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Authors: Galal H. Senussi, Muamar Benisa, Sanja Vasin

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In our business field today, one of the most important issues for any enterprises is cost minimization and profit maximization. Second issue is how to develop a strong and capable model that is able to give us desired forecasting of these two issues. Many researches deal with these issues using different methods. In this study, we developed a model for multi-criteria production program optimization, integrated with Artificial Neural Network. The prediction of the production cost and profit per unit of a product, dealing with two obverse functions at same time can be extremely difficult, especially if there is a great amount of conflict information about production parameters. Feed-Forward Neural Networks are suitable for generalization, which means that the network will generate a proper output as a result to input it has never seen. Therefore, with small set of examples the network will adjust its weight coefficients so the input will generate a proper output. This essential characteristic is of the most important abilities enabling this network to be used in variety of problems spreading from engineering to finance etc. From our results as we will see later, Feed-Forward Neural Networks has a strong ability and capability to map inputs into desired outputs.

Keywords: project profitability, multi-objective optimization, genetic algorithm, Pareto set, neural networks

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Authors: Duc Dong Do, Ngoc Ha Tran, Thanh Hai Dang, Cao Cuong Dang, Xuan Huan Hoang

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Global aligning two protein-protein interaction networks is an essentially important task in bioinformatics/computational biology field of study. It is a challenging and widely studied research topic in recent years. Accurately aligned networks allow us to identify functional modules of proteins and/ororthologous proteins from which unknown functions of a protein can be inferred. We here introduce a novel efficient heuristic global network alignment algorithm called FASTAn, including two phases: the first to construct an initial alignment and the second to improve such alignment by exerting a local optimization repeated procedure. The experimental results demonstrated that FASTAn outperformed the state-of-the-art global network alignment algorithm namely SPINAL in terms of both commonly used objective scores and the run-time.

Keywords: FASTAn, Heuristic algorithm, biological network alignment, protein-protein interaction networks

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: Yamin Sayyari

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In this paper, we generalized the Jensen's inequality for m-convex functions and also we present a correction of Jensen's inequality which is a better than the generalization of this inequality for m-convex functions. Finally, we have found new lower and new upper bounds for Jensen's discrete inequality.

Keywords: Jensen's inequality, m-convex function, Convex function, Inequality

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Authors: Syed Umair Aziz, Muhammad Faheem, Sameer Hussain, Faraz Idris

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Content centric network is the network based on the mechanism of sending and receiving the data based on the interest and data request to the specified node (which has cached data). In this network, the security is bind with the content not with the host hence making it host independent and secure. In this network security is applied by taking content’s MAC (message authentication code) and encrypting it with the public key of the receiver. On the receiver end, the message is first verified and after verification message is saved and decrypted using the receiver's private key.

Keywords: content centric network, client-server, host security threats, message authentication code, named data network, network caching, peer-to-peer

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Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

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Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

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