Search results for: selective mutation

Authors: Sung Hoon Jung

Abstract:

In this paper, we propose a selective mutation method for improving the performances of genetic algorithms. In selective mutation, individuals are first ranked and then additionally mutated one bit in a part of their strings which is selected corresponding to their ranks. This selective mutation helps genetic algorithms to fast approach the global optimum and to quickly escape local optima. This results in increasing the performances of genetic algorithms. We measured the effects of selective mutation with four function optimization problems. It was found from extensive experiments that the selective mutation can significantly enhance the performances of genetic algorithms.

Keywords: Genetic algorithm, selective mutation, function optimization

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Authors: Mike Sewell, Jagath Samarabandu, Ranga Rodrigo, Kenneth McIsaac

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A novel method of individual level adaptive mutation rate control called the rank-scaled mutation rate for genetic algorithms is introduced. The rank-scaled mutation rate controlled genetic algorithm varies the mutation parameters based on the rank of each individual within the population. Thereby the distribution of the fitness of the papulation is taken into consideration in forming the new mutation rates. The best fit mutate at the lowest rate and the least fit mutate at the highest rate. The complexity of the algorithm is of the order of an individual adaptation scheme and is lower than that of a self-adaptation scheme. The proposed algorithm is tested on two common problems, namely, numerical optimization of a function and the traveling salesman problem. The results show that the proposed algorithm outperforms both the fixed and deterministic mutation rate schemes. It is best suited for problems with several local optimum solutions without a high demand for excessive mutation rates.

Keywords: Genetic algorithms, mutation rate control, adaptive mutation.

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Authors: Eric Filiol

Abstract:

This paper presents a formalisation of the different existing code mutation techniques (polymorphism and metamorphism) by means of formal grammars. While very few theoretical results are known about the detection complexity of viral mutation techniques, we exhaustively address this critical issue by considering the Chomsky classification of formal grammars. This enables us to determine which family of code mutation techniques are likely to be detected or on the contrary are bound to remain undetected. As an illustration we then present, on a formal basis, a proof-of-concept metamorphic mutation engine denoted PB MOT, whose detection has been proven to be undecidable.

Keywords: Polymorphism, Metamorphism, Formal Grammars, Formal Languages, Language Decision, Code Mutation, Word Problem

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Authors: B. Falah, N. E. Abakouy

Abstract:

Due to its high computational cost, mutation testing has been neglected by researchers. Recently, many cost and mutants’ reduction techniques have been developed, improved, and experimented, but few of them has relied the possibility of reducing the cost of mutation testing on the program type of the application under test. This paper is a comparative study between four operators’ selection techniques (mutants sampling, class level operators, method level operators, and all operators’ selection) based on the program code type of each application under test. It aims at finding an alternative approach to reveal the effect of code type on mutation testing score. The result of our experiment shows that the program code type can affect the mutation score and that the programs using polymorphism are best suited to be tested with mutation testing.

Keywords: Equivalent mutant, killed mutant, mutation score, mutation testing, program code type.

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Authors: Emanuele Stomeo, Tatiana Kalganova, Cyrille Lambert

Abstract:

Evolvable hardware (EHW) refers to a selfreconfiguration hardware design, where the configuration is under the control of an evolutionary algorithm (EA). A lot of research has been done in this area several different EA have been introduced. Every time a specific EA is chosen for solving a particular problem, all its components, such as population size, initialization, selection mechanism, mutation rate, and genetic operators, should be selected in order to achieve the best results. In the last three decade a lot of research has been carried out in order to identify the best parameters for the EA-s components for different “test-problems". However different researchers propose different solutions. In this paper the behaviour of mutation rate on (1+λ) evolution strategy (ES) for designing logic circuits, which has not been done before, has been deeply analyzed. The mutation rate for an EHW system modifies values of the logic cell inputs, the cell type (for example from AND to NOR) and the circuit output. The behaviour of the mutation has been analyzed based on the number of generations, genotype redundancy and number of logic gates used for the evolved circuits. The experimental results found provide the behaviour of the mutation rate to be used during evolution for the design and optimization of logic circuits. The researches on the best mutation rate during the last 40 years are also summarized.

Keywords: Evolvable hardware, mutation rate, evolutionarycomputation, design of logic circuit.

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Authors: S. Khamsawang, S. Jiriwibhakorn

Abstract:

This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.

Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.

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Authors: Emanuele Stomeo, Tatiana Kalganova, Cyrille Lambert

Abstract:

Evolvable hardware (EHW) is a developing field that applies evolutionary algorithm (EA) to automatically design circuits, antennas, robot controllers etc. A lot of research has been done in this area and several different EAs have been introduced to tackle numerous problems, as scalability, evolvability etc. However every time a specific EA is chosen for solving a particular task, all its components, such as population size, initialization, selection mechanism, mutation rate, and genetic operators, should be selected in order to achieve the best results. In the last three decade the selection of the right parameters for the EA-s components for solving different “test-problems" has been investigated. In this paper the behaviour of mutation rate for designing logic circuits, which has not been done before, has been deeply analyzed. The mutation rate for an EHW system modifies the number of inputs of each logic gates, the functionality (for example from AND to NOR) and the connectivity between logic gates. The behaviour of the mutation has been analyzed based on the number of generations, genotype redundancy and number of logic gates for the evolved circuits. The experimental results found provide the behaviour of the mutation rate during evolution for the design and optimization of simple logic circuits. The experimental results propose the best mutation rate to be used for designing combinational logic circuits. The research presented is particular important for those who would like to implement a dynamic mutation rate inside the evolutionary algorithm for evolving digital circuits. The researches on the mutation rate during the last 40 years are also summarized.

Keywords: Design of logic circuit, evolutionary computation, evolvable hardware, mutation rate.

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Authors: Kristina Davoian, Wolfram-M. Lippe

Abstract:

Evolutionary Programming (EP) represents a methodology of Evolutionary Algorithms (EA) in which mutation is considered as a main reproduction operator. This paper presents a novel EP approach for Artificial Neural Networks (ANN) learning. The proposed strategy consists of two components: the self-adaptive, which contains phenotype information and the dynamic, which is described by genotype. Self-adaptation is achieved by the addition of a value, called the network weight, which depends on a total number of hidden layers and an average number of neurons in hidden layers. The dynamic component changes its value depending on the fitness of a chromosome, exposed to mutation. Thus, the mutation step size is controlled by two components, encapsulated in the algorithm, which adjust it according to the characteristics of a predefined ANN architecture and the fitness of a particular chromosome. The comparative analysis of the proposed approach and the classical EP (Gaussian mutation) showed, that that the significant acceleration of the evolution process is achieved by using both phenotype and genotype information in the mutation strategy.

Keywords: Artificial Neural Networks (ANN), Learning Theory, Evolutionary Programming (EP), Mutation, Self-Adaptation.

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Authors: Supachai Supmak, Yachai Limpiyakorn

Abstract:

Mutation testing can be applied for the quality assessment of test cases. Prioritization of mutation test generation has been a critical element of the industry practice that would contribute to the evaluation of test cases. The industry generally delivers the product under the condition of time to the market and thus, inevitably sacrifices software testing tasks, even though many test cases are required for software verification. This paper presents an approach of applying a social network centrality measure, PageRank, to prioritize mutation test generation. The source code with the highest values of PageRank, will be focused first when developing their test cases as these modules are vulnerable for defects or anomalies which may cause the consequent defects in many other associated modules. Moreover, the approach would help identify the reducible test cases in the test suite, still maintaining the same criteria as the original number of test cases.

Keywords: Software testing, mutation test, network centrality measure, test case prioritization.

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Authors: Konstantin Movsovic, Emanuele Stomeo, Tatiana Kalganova

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The evolutionary design of electronic circuits, or evolvable hardware, is a discipline that allows the user to automatically obtain the desired circuit design. The circuit configuration is under the control of evolutionary algorithms. Several researchers have used evolvable hardware to design electrical circuits. Every time that one particular algorithm is selected to carry out the evolution, it is necessary that all its parameters, such as mutation rate, population size, selection mechanisms etc. are tuned in order to achieve the best results during the evolution process. This paper investigates the abilities of evolution strategy to evolve digital logic circuits based on programmable logic array structures when different mutation rates are used. Several mutation rates (fixed and variable) are analyzed and compared with each other to outline the most appropriate choice to be used during the evolution of combinational logic circuits. The experimental results outlined in this paper are important as they could be used by every researcher who might need to use the evolutionary algorithm to design digital logic circuits.

Keywords: Evolvable hardware, evolutionary algorithm, digitallogic circuit, mutation rate.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Drago Jakovcevic, Mihovil Andelinovic, Igor Husak

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The aim of this paper is to explore the economic circumstances in which the selective credit policy, the least used instrument of four types of instruments on disposal to central banks, should be used. The most significant example includes the use of selective credit policies in response to the emergence of the global financial crisis by the FED. Specifics of the potential use of selective credit policies as the instigator of economic growth in Croatia, a small open economy, are determined by high euroization of financial system, fixed exchange rate and long-term trend growth of external debt that is related to the need to maintain high levels of foreign reserves. In such conditions, the classic forms of selective credit policies are unsuitable for the introduction. Several alternative approaches to implement selective credit policies are examined in this paper. Also, thorough analysis of distribution of selective monetary policy loans among economic sectors in Croatia is conducted in order to minimize the risk of investing funds and maximize the return, in order to influence the GDP growth.

Keywords: Global crisis, Selective credit policy, Small open economy.

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Authors: Huong M. T. Nguyen, Hoa A. P. Nguyen, Mai P. T. Nguyen, Ngoc D. Ngo, Van T. Ta, Hai T. Le, Chi V. Phan

Abstract:

Wilson’s disease (WD) is an autosomal recessive disorder of the copper metabolism, which is caused by a mutation in the copper-transporting P-type ATPase (ATP7B). The mechanism of this disease is the failure of hepatic excretion of copper to bile, and leads to copper deposits in the liver and other organs. The ATP7B gene is located on the long arm of chromosome 13 (13q14.3). This study aimed to investigate the gene mutation in the Vietnamese patients with WD, and make a presymptomatic diagnosis for their familial members. Forty-three WD patients and their 65 siblings were identified as having ATP7B gene mutations. Genomic DNA was extracted from peripheral blood samples; 21 exons and exon-intron boundaries of the ATP7B gene were analyzed by direct sequencing. We recognized four mutations ([R723=; H724Tfs*34], V1042Cfs*79, D1027H, and IVS6+3A>G) in the sum of 20 detectable mutations, accounting for 87.2% of the total. Mutation S105* was determined to have a high rate (32.6%) in this study. The hotspot regions of ATP7B were found at exons 2, 16, and 8, and intron 14, in 39.6 %, 11.6 %, 9.3%, and 7 % of patients, respectively. Among nine homozygote/compound heterozygote siblings of the patients with WD, three individuals were determined as asymptomatic by screening mutations of the probands. They would begin treatment after diagnosis. In conclusion, 20 different mutations were detected in 43 WD patients. Of this number, four novel mutations were explored, including [R723=; H724Tfs*34], V1042Cfs*79, D1027H, and IVS6+3A>G. The mutation S105* is the most prevalent and has been considered as a biomarker that can be used in a rapid detection assay for diagnosis of WD patients. Exons 2, 8, and 16, and intron 14 should be screened initially for WD patients in Vietnam. Based on risk profile for WD, genetic testing for presymptomatic patients is also useful in diagnosis and treatment.

Keywords: ATP7B gene, mutation detection, presymptomatic diagnosis, Vietnamese Wilson’s disease.

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Authors: Chrysline Margus N. Piñol, Jenifer DP. De Maligaya, Ahl G. Balitaon

Abstract:

Stable nonzero populations without random deaths caused by the Verhulst factor (Verhulst-free) are a rarity. Majority either grow without bounds or die of excessive harmful mutations. To delay the accumulation of bad genes or diseases, a new environmental parameter Γ is introduced in the simulation. Current results demonstrate that stability may be achieved by setting Γ = 0.1. These steady states approach a maximum size that scales inversely with reproduction age.

Keywords: Aging, mutation accumulation, population dynamics.

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Authors: Sushil Sarwa, Rajeev Kumar

Abstract:

The wireless mesh networks (WMNs) are emerging technology in wireless networking as they can serve large scale high speed internet access. Due to its wireless multi-hop feature, wireless mesh network is prone to suffer from many attacks, such as denial of service attack (DoS). We consider a special case of DoS attack which is selective forwarding attack (a.k.a. gray hole attack). In such attack, a misbehaving mesh router selectively drops the packets it receives rom its predecessor mesh router. It is very hard to detect that packet loss is due to medium access collision, bad channel quality or because of selective forwarding attack. In this paper, we present a review of detection algorithms of selective forwarding attack and discuss their advantage & disadvantage. Finally we conclude this paper with open research issues and challenges.

Keywords: CAD algorithm, CHEMAS, selective forwarding attack, watchdog & pathrater, wireless mesh network.

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Authors: Xun Liang

Abstract:

In this paper, we probe into the traffic assignment problem by the chromosome-learning-based path finding method in simulation, which is to model the driver' behavior in the with-in-a-day process. By simply making a combination and a change of the traffic route chromosomes, the driver at the intersection chooses his next route. The various crossover and mutation rules are proposed with extensive examples.

Keywords: Chromosome learning, crossover, mutation, traffic path finding.

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Authors: Suresh Palla, Suresh Vanguri, Anitha, B. N. Mohapatra

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This paper presents the results of the study on the estimation of fly ash, slag and cement contents in blended and composite cements by selective dissolution method. Types of cement samples investigated include Ordinary Portland Cement (OPC) with fly ash as performance improver, OPC with slag as performance improver, Portland Pozzolana Cement (PPC), Portland Slag Cement (PSC) and composite cement confirming to respective Indian Standards. Slag and OPC contents in PSC were estimated by selectively dissolving OPC in stage 1 and selectively dissolving slag in stage 2. In the case of composite cement sample, the percentage of cement, slag and fly ash were estimated systematically by selective dissolution of cement, slag and fly ash in three stages. In the first stage, cement is dissolved and separated by leaving the residue of slag and fly ash, designated as R1. The second stage involves gravimetric estimation of fractions of OPC, residue and selective dissolution of fly ash and slag contents. Fly ash content, R2 was estimated through gravimetric analysis. Thereafter, the difference between the R1 and R2 is considered as slag content. The obtained results of cement, fly ash and slag using selective dissolution method showed 10% of standard deviation with the corresponding percentage of respective constituents. The results suggest that this selective dissolution method can be successfully used for estimation of OPC and Supplementary Cementitious material (SCM) contents in different types of cements.

Keywords: Selective dissolution method, fly ash, Ground Granulated blast furnace slag, EDTA.

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Authors: Mohammad Shams Esfand Abadi, Nader Hadizadeh Kashani, Vahid Mehrdad

Abstract:

In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.

Keywords: Adaptive filter, affine projection, selective regressor.

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Authors: Mohammad Ali Tabarzad, Caro Lucas, Ali Hamzeh

Abstract:

Adaptive Genetic Algorithms extend the Standard Gas to use dynamic procedures to apply evolutionary operators such as crossover, mutation and selection. In this paper, we try to propose a new adaptive genetic algorithm, which is based on the statistical information of the population as a guideline to tune its crossover, selection and mutation operators. This algorithms is called Statistical Genetic Algorithm and is compared with traditional GA in some benchmark problems.

Keywords: Genetic Algorithms, Statistical Information ofthe Population, PAUX, SSO.

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Authors: Samia Alblwi, Amani Ayad

Abstract:

Mutation testing is the art of generating syntactic variations of a base program and checking whether a candidate test suite can identify all the mutants that are not semantically equivalent to the base; this technique can be used to assess the quality of test suite. One of the main obstacles to the widespread use of mutation testing is cost, as even small programs (a few dozen lines of code) can give rise to a large number of mutants (up to hundreds); this has created an incentive to seek to reduce the number of mutants while preserving their collective effectiveness. Two criteria have been used to reduce the size of mutant sets: equivalence, which aims to partition the set of mutants into equivalence classes modulo semantic equivalence, and selecting one representative per class; and, subsumption, which aims to define a partial ordering among mutants that ranks mutants by effectiveness and seeks to select maximal elements in this ordering. In this paper, we analyze these two policies using analytical and empirical criteria.

Keywords: Mutation testing, mutant sets, mutant equivalence, mutant subsumption, mutant set minimization.

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Authors: J. Tengrang, T. Rungrotmongkol, S. Hannongbua

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Every 2-3 years the influenza B virus serves epidemics. Neuraminidase (NA) is an important target for influenza drug design. Although, oseltamivir, an oral neuraminidase drug, has been shown good inhibitory efficiency against wild-type of influenza B virus, the lower susceptibility to the R152K mutation has been reported. Better understanding of oseltamivir efficiency and resistance toward the influenza B NA wild-type and R152K mutant, respectively, could be useful for rational drug design. Here, two complex systems of wild-type and R152K NAs with oseltamivir bound were studied using molecular dynamics (MD) simulations. Based on 5-ns MD simulation, the loss of notable hydrogen bond and decrease in per-residue decomposition energy from the mutated residue K152 contributed to drug compared to those of R152 in wildtype were found to be a primary source of high-level of oseltamivir resistance due to the R152K mutation.

Keywords: Influenza B neuraminidase, Molecular dynamics simulation, Oseltamivir resistance, R152K mutant

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Authors: Chien-Cheng Kuo

Abstract:

We design and discuss metal-dielectric antireflection coating on metallic substrates for Solar Selective Absorbers of Concentrating Solar Power Systems. The average reflectance is 8.5% at 400-3000nm and 84.4% at 3000nm-10000nm of the metal-dielectric structure.

Keywords: Concentrating solar power systems, solar thermal, solar selective absorber, absorptance, emittance.

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Authors: Danial Husseinzadeh

Abstract:

A new supported liquid membrane (SLM) system for the selective transport of VO2 + ions was prepared in this present work. The SLM was a thin porous polyvinylidene difluoride (PVDF) membrane soaked with Di-(2-ethylhexyl) phosphoric acid (D2EHPA) as mobile carrier in Xylene as organic solvent. D2EHPA acts as a highly selective carrier for the uphill transport of VO2 + ions through the SLM. The transport of VO2 + ions reached to 64%. In the presence of P2O7-2 ion as suitable masking agent in the feed solution, the interfering effects of other cations were eliminated.

Keywords: Facilitated ion transport, Membrane characteristics, Supported liquid membranes, Vanadium.

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Authors: Zhoucheng Bao, Haiyan Zhu, Tingting Pang, Zuling Wang

Abstract:

This paper presents a multi population Differential Evolution (DE) with adaptive mutation and local search for global optimization, named AMMADE in order to better coordinate the cooperation between the populations and the rational use of resources. In AMMADE, the population is divided based on the Euclidean distance sorting method at each generation to appropriately coordinate the cooperation between subpopulations and the usage of resources, such that the best-performed subpopulation will get more computing resources in the next generation. Further, an adaptive local search strategy is employed on the best-performed subpopulation to achieve a balanced search. The proposed algorithm has been tested by solving optimization problems taken from CEC2014 benchmark problems. Experimental results show that our algorithm can achieve a competitive or better result than related methods. The results also confirm the significance of devised strategies in the proposed algorithm.

Keywords: Differential evolution, multi-mutation strategies, memetic algorithm, adaptive local search.

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Authors: Panpan Xu, Shulin Sui

Abstract:

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: Mohammad Rezaee, Mohammad Kazemeini, Ali Morad Rashidi, Moslem Fattahi

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Selective oxidation of H2S to elemental sulfur in a fixed bed reactor over newly synthesized alumina nanocatalysts was physio-chemically investigated and results compared with a commercial Claus catalyst. Amongst these new materials, Al2O3- supported sodium oxide prepared with wet chemical technique and Al2O3 nanocatalyst prepared with spray pyrolysis method were the most active catalysts for selective oxidation of H2S to elemental sulfur. Other prepared nanocatalysts were quickly deactivated, mainly due to the interaction with H2S and conversion into sulfides.

Keywords: H2S, Claus process, Al2O3, Spray pyrolysis method, Wet chemical technique

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Authors: Omar M. Sallabi, Younis El-Haddad

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The Genetic Algorithm (GA) is one of the most important methods used to solve many combinatorial optimization problems. Therefore, many researchers have tried to improve the GA by using different methods and operations in order to find the optimal solution within reasonable time. This paper proposes an improved GA (IGA), where the new crossover operation, population reformulates operation, multi mutation operation, partial local optimal mutation operation, and rearrangement operation are used to solve the Traveling Salesman Problem. The proposed IGA was then compared with three GAs, which use different crossover operations and mutations. The results of this comparison show that the IGA can achieve better results for the solutions in a faster time.

Keywords: AI, Genetic algorithms, TSP.

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Authors: Priya Bhakat

Abstract:

A son in every Hindu society pays his own father the debt and he owes him for his own life whereas a girl child is treated as a burden mainly in case of first child. Even today in India we have many societies which does not welcome girl child. Although there is an increase in overall sex ratio, there is a continuous decline in child sex ratio. This paper focuses on issues of sex selective abortion in Rajasthan based on secondary data. It is found that 90.0 percentages of women in Rajasthan wants at least one son. Around 34.3 percentages of women wants more sons than daughters and only 1.5 percentages of women wants more daughters than sons. It is very common among the rich and educated people.

Keywords: Rajasthan, Family Planning Program (FPP), Sex Selective Abortion (SSA), Sex Ratio at Birth (SRB).

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Authors: Atisthan Wuttimanop, Suchada Rianmora

Abstract:

To support design process for launching the product on time, reverse engineering (RE) process has been introduced for quickly generating 3D CAD model from its physical object. The accuracy of the 3D CAD model depends upon the data acquisition technique selected, contact or non-contact methods. In order to reduce times used for acquiring surface and eliminating noises, the automated selective acquisition system has been developed and presented in this research as the alternative channel for non-contact acquisition technique where the data is selectively and locally scanned contour by contour without performing data reduction process. The results present as the organized contour points which are directly used to generate 3D virtual model. The comparison between the proposed technique and another non-contact scanning technique has been presented and discussed.

Keywords: Automated selective acquisition system, Non-contact acquisition, Reverse engineering, 3D scanners.

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Authors: S. Selvaperumal, M. S. Sivagamasundari

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In this paper, selective harmonic elimination pulse width modulation technique is employed to eliminate lower order harmonics like third by determination of solving non-linear equations. The cascaded H-bridge five level inverter is driven by the Peripheral Interface Controlled (PIC) Microcontroller 16F877A. The performance of single phase cascaded H-bridge five level inverter with relevant to harmonics and a variety of switches with solar cell as its input source is simulated by employing MATLAB/Simulink. A hardware model is developed to verify the performance of the developed system.

Keywords: Multilevel inverter, cascaded H-Bridge multilevel inverter, total harmonic distortion, selective harmonic elimination pulse width modulation, MATLAB.

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