Search results for: rate of convergence

Authors: Alina Mirza, Sumrin M. Kabir, Shahzad A. Sheikh

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The Orthogonal Frequency Division Multiplexing (OFDM) with high data rate, high spectral efficiency and its ability to mitigate the effects of multipath makes them most suitable in wireless application. Impulsive noise distorts the OFDM transmission and therefore methods must be investigated to suppress this noise. In this paper, a State Space Recursive Least Square (SSRLS) algorithm based adaptive impulsive noise suppressor for OFDM communication system is proposed. And a comparison with another adaptive algorithm is conducted. The state space model-dependent recursive parameters of proposed scheme enables to achieve steady state mean squared error (MSE), low bit error rate (BER), and faster convergence than that of some of existing algorithm.

Keywords: OFDM, impulsive noise, SSRLS, BER

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Authors: Huai-Cong Liu，Tae Chul Jeong，Ju Lee

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This paper describes characteristic analysis of a synchronous reluctance motor (SynRM)’s rotor with the Multi-segment and Multi-layer structure. The magnetic-saturation phenomenon in SynRM is often appeared. Therefore, when modeling analysis of SynRM the calculation of nonlinear magnetic field needs to be considered. An important influence factor on the convergence process is how to determine the relative permeability. An improved method, which ensures the calculation, is convergence by linear iterative method for saturated magnetic field. If there are inflection points on the magnetic curve,an optimum convergence method of solution for nonlinear magnetic field was provided. Then the equivalent magnetic circuit is calculated, and d,q-axis inductance can be got. At last, this process is applied to design a 7.5Kw SynRM and its validity is verified by comparing with the result of finite element method (FEM) and experimental test data.

Keywords: SynRM, magnetic-saturation, magnetic circuit, analytical modeling

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Authors: Muhammad Younis

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A ternary 4-point approximating non-stationary subdivision scheme has been introduced that generates the family of $C^2$ limiting curves. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing 4-point ternary approximating schemes, which shows that the limit curves of the proposed scheme behave more pleasantly and can generate conic sections as well.

Keywords: ternary, non-stationary, approximation subdivision scheme, convergence and smoothness

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

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This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: convection flow, similarity, numerical analysis, spectral method, Williamson nanofluid, internal heat generation

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Inten Meutia, Emylia Yuniarti

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The objective of this study is to analyze the effects of interest rate, the rate of return of Islamic banks on the amount of mudarabah deposits in Islamic banks. In analyzing the effect of rate of return in the Islamic banks and interest rate risk in the conventional banks, the 1-month Islamic deposit rate of return and 1 month fixed deposit interest rate of a total Islamic deposit are considered. Using data covering the period from January 2010 to Sepember 2013, the study applies the regression analysis to analyze the effect between variable and independence t-test to analyze the mean difference between rate of return and rate of interest. Regression analysis shows that rate of return have significantly negative influence on mudarabah deposits, while interest rate have negative influence but not significant. The result of independent t test shows that the interest rate is not different from the rate of return in Islamic Bank. It supports the hyphotesis that rate of return in Islamic banking mimic rate of interest in conventional bank. The results of the study have important implications on the risk management practices of the Islamic banks in Indonesia.

Keywords: conventional bank, interest rate, Islamic bank, rate of return

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Authors: Swarn Singh, Suruchi Singh

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In this paper, we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme. In this paper we present a fourth order two level implicit finite difference scheme for 1D Pennes bio-heat equation. Unconditional stability and convergence of the proposed scheme is discussed. Numerical results are obtained to demonstrate the efficiency of the scheme.

Keywords: convergence, finite difference scheme, Pennes bio-heat equation, stability

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Authors: Ebert Brea

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We propose a novel direct search algorithm for identifying at least a local minimum of mixed integer nonlinear unconstrained optimization problems. The Mixed Integer Randomized Pattern Search Algorithm (MIRPSA), so-called by the author, is based on a randomized pattern search, which is modified by the MIRPSA for finding at least a local minimum of our problem. The MIRPSA has two main operations over the randomized pattern search: moving operation and shrinking operation. Each operation is carried out by the algorithm when a set of conditions is held. The convergence properties of the MIRPSA is analyzed using a Markov chain approach, which is represented by an infinite countable set of state space λ, where each state d(q) is defined by a measure of the qth randomized pattern search Hq, for all q in N. According to the algorithm, when a moving operation is carried out on the qth randomized pattern search Hq, the MIRPSA holds its state. Meanwhile, if the MIRPSA carries out a shrinking operation over the qth randomized pattern search Hq, the algorithm will visit the next state, this is, a shrinking operation at the qth state causes a changing of the qth state into (q+1)th state. It is worthwhile pointing out that the MIRPSA never goes back to any visited states because the MIRPSA only visits any qth by shrinking operations. In this article, we describe the MIRPSA for mixed integer nonlinear unconstrained optimization problems for doing a deep study of its convergence properties using Markov chain viewpoint. We herein include a low dimension case for showing more details of the MIRPSA, when the algorithm is used for identifying the minimum of a mixed integer quadratic function. Besides, numerical examples are also shown in order to measure the performance of the MIRPSA.

Keywords: direct search, mixed integer optimization, random search, convergence, Markov chain

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Authors: Israt Jahan Eshita

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Flows developed between two parallel disks have many engineering applications. Two types of non-swirling flows can be generated in such a domain. One is purely source flow in disc type domain (outward flow). Other is purely sink flow in disc type domain (inward flow). This situation often appears in some turbo machinery components such as air bearings, heat exchanger, radial diffuser, vortex gyroscope, disc valves, and viscosity meters. The main goal of this paper is to show the mesh convergence, because mesh convergence saves time, and economical to run and increase the efficiency of modeling for both sink and source flow. Then flow field is resolved using a very fine mesh near-wall, using enhanced wall treatment. After that we are going to compare this flow using standard k-epsilon, RNG k-epsilon turbulence models. Lastly compare some experimental data with numerical solution for sink flow. The good agreement of numerical solution with the experimental works validates the current modeling.

Keywords: hydraulic diameter, k-epsilon model, meshes convergence, Reynolds number, RNG model, sink flow, source flow, wall y+

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Authors: Mukesh Kumar Shah, Tushar Gupta

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An Upgraded Cuckoo Search Algorithm is proposed here to solve optimization problems based on the improvements made in the earlier versions of Cuckoo Search Algorithm. Short comings of the earlier versions like slow convergence, trap in local optima improved in the proposed version by random initialization of solution by suggesting an Improved Lambda Iteration Relaxation method, Random Gaussian Distribution Walk to improve local search and further proposing Greedy Selection to accelerate to optimized solution quickly and by “Study Nearby Strategy” to improve global search performance by avoiding trapping to local optima. It is further proposed to generate better solution by Crossover Operation. The proposed strategy used in algorithm shows superiority in terms of high convergence speed over several classical algorithms. Three standard algorithms were tested on a 6-generator standard test system and the results are presented which clearly demonstrate its superiority over other established algorithms. The algorithm is also capable of handling higher unit systems.

Keywords: economic dispatch, gaussian selection operator, prohibited operating zones, ramp rate limits

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Authors: Prashant Pandey

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In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: Tri Wijayanti Septiarini, Agus Maman Abadi, Muhammad Rifki Taufik

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The exchange rate of IDR/USD can be the indicator to analysis Indonesian economy. The exchange rate as a important factor because it has big effect in Indonesian economy overall. So, it needs the analysis data of exchange rate. There is decomposition data of exchange rate of IDR/USD to be frequency and time. It can help the government to monitor the Indonesian economy. This method is very effective to identify the case, have high accurate result and have simple structure. In this paper, data of exchange rate that used is weekly data from December 17, 2010 until November 11, 2014.

Keywords: the exchange rate, fuzzy mamdani, discrete wavelet transforms, fuzzy wavelet

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Authors: Keunho Park, Sunghwan Jeong

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The 4th Industrial Revolution, the next-generation industrial revolution, which is made up of convergence of information and communication technology (ICT), is no exception to the livestock industry, and various studies are being conducted to apply the livestock smart farm. In order to monitor livestock using sensors, it is necessary to drill holes in the organs such as the nose, ears, and even the stomach of the livestock to wear or insert the sensor into the livestock. This increases the stress of livestock, which in turn lowers the quality of livestock products or raises the issue of animal ethics, which has become a major issue in recent years. In this paper, we conducted a study to monitor livestock activity based on vision technology, effectively monitoring livestock activity without increasing animal stress and violating animal ethics. The movement rate was calculated based on the difference images between the frames, and the livestock activity was evaluated. As a result, the average F1-score was 96.67.

Keywords: barn monitoring, livestock, machine vision, smart farm

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Authors: Safeer Hussain Khan

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In this paper, we introduce a two-step iterative algorithm to prove a strong convergence result for approximating common fixed points of three contractive-like operators. Our algorithm basically generalizes an existing algorithm..Our iterative algorithm also contains two famous iterative algorithms: Mann iterative algorithm and Ishikawa iterative algorithm. Thus our result generalizes the corresponding results proved for the above three iterative algorithms to a class of more general operators. At the end, we remark that nothing prevents us to extend our result to the case of the iterative algorithm with error terms.

Keywords: contractive-like operator, iterative algorithm, fixed point, strong convergence

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Authors: Omenogor, Happy Dumbi

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This paper examines the areas of convergence and divergence between English and Ųkwųanį (a language in Nigeria) vowel systems with particular emphasis on the front vowels. It specifies areas of difficulty for the average Ųkwųanį users of English and Ųkwųanį L1 users of English as a second language. The paper explains the nature of contrastive analysis, the geographical locations where Ųkwųanį is spoken as mother tongue as well as English and Ųkwųanį front vowels. The principles of establishing phonemes, minimal pairs in Ųkwųanį as well as the vowel charts in both languages are among the issues highlighted in this paper.

Keywords: convergence, divergence, English, Ukwųanį

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Authors: Mandy Tao Benec

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Propaganda, understood as a ‘deliberate attempt to persuade people to think and behave in a desired way’, contributes to the fabric of mass media discourse as an important component, albeit often under various alternative expressions except ‘propaganda’. When the word ‘propaganda’ does appear in the mainstream media of the West, it is often selectively applied upon undesiring parties such as China, the North Korea, Russia’s Putin, or terrorists, etc.. This attitude reveals an ‘us verse them’ mentality; and a presupposition that propaganda is something only ‘they’ do whilst ‘we’ do not. This phenomenon not only runs in danger of generating political naivety, but also calls for the necessity of re-examining propaganda which will benefit from analysing it in contrasting social and political environments. Therefore, this paper aims to compare how propaganda has been understood and put in practice both in the Anglo-American context and by the Chinese Communist Party (CCP). By revealing the convergence and divergence of the propaganda discourses between China and the West, it will help clarify the misconception and misunderstanding of the term. Historical narrative analysis and critical discourse analysis are the main methodologies. By carefully examining data from academic research on propaganda in both English and Chinese, the landscape of how propaganda is defined throughout different eras is mapped, with special attention paid to analysing the parallelism and/or correspondence between China and the West when applicable. Meanwhile, critically analysing the official documents such as speeches and guidelines for propaganda administration given by top-rank CCP leaders will help reveal that in contrast to the West’s ‘us-them’ mentality, China sees oneself in no difference with the Western democracies when propaganda is concerned. Major findings of this study will identify a series of convergence and divergence between Chinese and Western propaganda discourses, and the relationship between propaganda the ‘signified’ (its essence) and propaganda the ‘signifier’ (the term itself), including (yet not limited to): 1) convergence in China catching up with the West, acknowledging the perceived pejorative connotation of the term 2) divergence in propaganda activities disassociated from the term in the West; and convergence in adopting such practice when China following suit in its external propaganda towards the West 3) convergence in utilising alternative notions to replace ‘propaganda’, first by the West, then imported and incorporated enthusiastically by China into its propaganda discourse 4) divergence between China’s internal and external propaganda and the subsequent differentiation between in which contexts the CCP sees fit to utilise the concept 5) convergence between China and the West in their English language propaganda discourses, whilst simultaneous divergence in their presuppositions: ‘usthem’ by the West and ‘we are the same’ by China. To conclude, this paper will contribute to the study of propaganda and its discourse by analysing how propaganda is understood and utilised in both worlds, and hence to uncover the discourse power struggle between the two, which contributes to the propaganda discourse itself. Hence, to untie the misconception of propaganda.

Keywords: China, discourse, power, propaganda

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Authors: Ghada Abo-Zaid

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Introduction: Oil is one of the most income source in Bahrain. Low oil price influence on the economy growth and the investment rate in Bahrain. For example, the economic growth was 3.7% in 2012, and it reduced to 2.9% in 2015. Investment rate was 9.8% in 2012, and it is reduced to be 5.9% and -12.1% in 2014 and 2015, respectively. The inflation rate is increased to the peak point in 2013 with 3.3 %. Objectives: The objectives here are to build statistical models to examine the effect of the interest rate inflation rate on the growth economy in Bahrain from 2000 to 2018. Methods: This study based on 18 years, and the multiple regression model is used for the analysis. All of the missing data are omitted from the analysis. Results: Regression model is used to examine the association between the Growth national product (GNP), the inflation rate, and real interest rate. We found that (i) Increase the real interest rate decrease the GNP. (ii) Increase the inflation rate does not effect on the growth economy in Bahrain since the average of the inflation rate was almost 2%, and this is considered as a low percentage. Conclusion: There is a positive impact of the real interest rate on the GNP in Bahrain. While the inflation rate does not show any negative influence on the GNP as the inflation rate was not large enough to effect negatively on the economy growth rate in Bahrain.

Keywords: growth national product, egypt, regression model, interest rate

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Authors: B. Siva Kumar Reddy, B. Lakshmi

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WiMAX has adopted an Adaptive Modulation and Coding (AMC) in OFDM to endure higher data rates and error free transmission. AMC schemes employ the Channel State Information (CSI) to efficiently utilize the channel and maximize the throughput and for better spectral efficiency. This CSI has given to the transmitter by the channel estimators. In this paper, LSE (Least Square Error) and MMSE (Minimum Mean square Error) estimators are suggested and BER (Bit Error Rate) performance has been analyzed. Channel equalization is also integrated with with AMC-OFDM system and presented with Constant Modulus Algorithm (CMA) and Least Mean Square (LMS) algorithms with convergence rates analysis. Simulation results proved that increment in modulation scheme size causes to improvement in throughput along with BER value. There is a trade-off among modulation size, throughput, BER value and spectral efficiency. Results also reported the requirement of channel estimation and equalization in high data rate systems.

Keywords: AMC, CSI, CMA, OFDM, OFDMA, WiMAX

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: Amirreza Attarzadeh

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This paper aims to investigate the relationship between economic variables, e.g., inflation rate, interest rate, trade openness and the growth rate of GDP, with domestic investment. The present study also draws on conceptual economy related theories to verify the negative effect of interest rates on domestic investment. However, trade openness and growth rate had a positive correlation, and the inflation rate may have a positive or negative impact on domestic investment.

Keywords: inflation rate, growth rate of GDP, interest rate and trade openness, domestic investment

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Authors: Himanshu Shekhar Maharana, S. K .Dash

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Economic Load Dispatch (ELD) proves to be a vital optimization process in electric power system for allocating generation amongst various units to compute the cost of generation, the cost of emission involving global warming gases like sulphur dioxide, nitrous oxide and carbon monoxide etc. In this dissertation, we emphasize ramp rate constriction factor based particle swarm optimization (RRCPSO) for analyzing various performance objectives, namely cost of generation, cost of emission, and a dual objective function involving both these objectives through the experimental simulated results. A 6-unit 30 bus IEEE test case system has been utilized for simulating the results involving improved weight factor advanced ramp rate limit constraints for optimizing total cost of generation and emission. This method increases the tendency of particles to venture into the solution space to ameliorate their convergence rates. Earlier works through dispersed PSO (DPSO) and constriction factor based PSO (CPSO) give rise to comparatively higher computational time and less good optimal solution at par with current dissertation. This paper deals with ramp rate and constriction factor based well defined ramp rate PSO to compute various objectives namely cost, emission and total objective etc. and compares the result with DPSO and weight improved PSO (WIPSO) techniques illustrating lesser computational time and better optimal solution. 

Keywords: economic load dispatch (ELD), constriction factor based particle swarm optimization (CPSO), dispersed particle swarm optimization (DPSO), weight improved particle swarm optimization (WIPSO), ramp rate and constriction factor based particle swarm optimization (RRCPSO)

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Authors: Sreeni K. R.

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Sarvathobhadram-Organic–Farmers Cooperative was helpful in supporting small and marginal farmers in customizing, adapting, and tailoring the system to their specific requirements. The Farmers Club, which has 50 members, was founded in May 2020 to create additional cash while also encouraging farmers to shift to organic farming. The club's mission is to ensure food security, livelihood, and entrepreneurship in the Anthikad Block Panchayat. The project addressed climate change and resilience, collaborating with government departments and utilizing convergence to maximize the schemes accessible to farmers in panchayath. The transformation was sluggish initially, but it accelerated over time, indicating that farmers have variable levels of satisfaction based on a variety of circumstances. This paper examines the changing trend in the area after adopting organic farming using the SRI method, the increase in production, and the success of the convergence method. It also attempts to find out various constraints faced by farmers during the paradigm shift from conventional methods to organic, and the results have proven that SRI should be considered as a potential cultivation method for all farmer's groups (Padasekharam).

Keywords: Sarvathobhadram-Organic, Thanniyam gram Panchayat, organic Joythi rice, convergence method, Jeevamirtham, natural methods, system of rice intensification

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Authors: M. Macchiaroli, L. Dolores, V. Pellecchia

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With the recent Resolution n. 580/2019/R/idr, the Italian Regulatory Authority for Energy, Networks, and Environment (ARERA) for the Urban Water Management has introduced, for water managements characterized by persistent critical issues regarding the planning and organization of the service and the implementation of the necessary interventions for the improvement of infrastructures and management quality, a new mechanism for determining tariffs: the regulatory scheme of Convergence. The aim of this regulatory scheme is the overcoming of the Water Service Divided in order to improve the stability of the local institutional structures, technical quality, contractual quality, as well as in order to guarantee transparency elements for Users of the Service. Convergence scheme presupposes the identification of the cost items to be considered in the tariff in parametric terms, distinguishing three possible cases according to the type of historical data available to the Manager. The study, in particular, focuses on operations that have neither data on tariff revenues nor data on operating costs. In this case, the Manager's Constraint on Revenues (VRG) is estimated on the basis of a reference benchmark and becomes the starting point for defining the structure of the tariff classes, in compliance with the TICSI provisions (Integrated Text for tariff classes, ARERA's Resolution n. 665/2017/R/idr). The proposed model implements the recent studies on optimization models for the definition of tariff classes in compliance with the constraints dictated by TICSI in the application of the Convergence mechanism, proposing itself as a support tool for the Managers and the local water regulatory Authority in the decision-making process.

Keywords: decision-making process, economic evaluation of projects, optimizing tools, urban water management, water tariff

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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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Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

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Authors: Young Hee Geum

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In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.

Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Ferzat Anka

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Many types of problems can be solved using traditional analytical methods. However, these methods take a long time and cause inefficient use of resources. In particular, different approaches may be required in solving complex and global engineering problems that we frequently encounter in real life. The bigger and more complex a problem, the harder it is to solve. Such problems are called Nondeterministic Polynomial time (NP-hard) in the literature. The main reasons for recommending different metaheuristic algorithms for various problems are the use of simple concepts, the use of simple mathematical equations and structures, the use of non-derivative mechanisms, the avoidance of local optima, and their fast convergence. They are also flexible, as they can be applied to different problems without very specific modifications. Thanks to these features, it can be easily embedded even in many hardware devices. Accordingly, this approach can also be used in trend application areas such as IoT, big data, and parallel structures. Indeed, the metaheuristic approaches are algorithms that return near-optimal results for solving large-scale optimization problems. This study is focused on the new metaheuristic method that has been merged with the chaotic approach. It is based on the chaos theorem and helps relevant algorithms to improve the diversity of the population and fast convergence. This approach is based on Chimp Optimization Algorithm (ChOA), that is a recently introduced metaheuristic algorithm inspired by nature. This algorithm identified four types of chimpanzee groups: attacker, barrier, chaser, and driver, and proposed a suitable mathematical model for them based on the various intelligence and sexual motivations of chimpanzees. However, this algorithm is not more successful in the convergence rate and escaping of the local optimum trap in solving high-dimensional problems. Although it and some of its variants use some strategies to overcome these problems, it is observed that it is not sufficient. Therefore, in this study, a newly expanded variant is described. In the algorithm called Ex-ChOA, hybrid models are proposed for position updates of search agents, and a dynamic switching mechanism is provided for transition phases. This flexible structure solves the slow convergence problem of ChOA and improves its accuracy in multidimensional problems. Therefore, it tries to achieve success in solving global, complex, and constrained problems. The main contribution of this study is 1) It improves the accuracy and solves the slow convergence problem of the ChOA. 2) It proposes new hybrid movement strategy models for position updates of search agents. 3) It provides success in solving global, complex, and constrained problems. 4) It provides a dynamic switching mechanism between phases. The performance of the Ex-ChOA algorithm is analyzed on a total of 8 benchmark functions, as well as a total of 2 classical and constrained engineering problems. The proposed algorithm is compared with the ChoA, and several well-known variants (Weighted-ChoA, Enhanced-ChoA) are used. In addition, an Improved algorithm from the Grey Wolf Optimizer (I-GWO) method is chosen for comparison since the working model is similar. The obtained results depict that the proposed algorithm performs better or equivalently to the compared algorithms.

Keywords: optimization, metaheuristic, chimp optimization algorithm, engineering constrained problems

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Authors: Umar Yusuf Batsari

Abstract:

Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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