Search results for: normalized normal constraint method

Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat

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Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.

Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.

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Authors: Nemat Abazari, Reza Abazari

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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: M. Mokhtarzadeh, M. Taheri Qomi, M. Nikafrooz, A. Atashafrooz

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The purpose of the present study was to investigate the effectiveness of using motion graphics as a learning medium on training hearing aids maintenance skills to hearing-impaired children. The statistical population of this study consisted of all children with hearing loss in Ahvaz city, at age 4 to 7 years old. As the sample, 60, whom were selected by multistage random sampling, were randomly assigned to two groups; experimental (30 children) and control (30 children) groups. The research method was experimental and the design was pretest-posttest with the control group. The intervention consisted of a 2-minute motion graphics clip to train hearing aids maintenance skills. Data were collected using a 9-question researcher-made questionnaire. The data were analyzed by using one-way analysis of covariance. Results showed that the training of hearing aids maintenance skills with motion graphics was significantly effective for those children. The results of this study can be used by educators, teachers, professionals, and parents to train children with disabilities or normal students.

Keywords: Hearing-impaired children, hearing aids, hearing aids maintenance skill, and motion graphics.

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee

Abstract:

Adopting Most Advantageous Tender (MAT) for the government procurement projects has become popular in Taiwan. As time pass by, the problems of MAT has appeared gradually. People condemn two points that are the result might be manipulated by a single committee member’s partiality and how to make a fair decision when the winner has two or more. Arrow’s Impossibility Theorem proposed that the best scoring method should meet the four reasonable criteria. According to these four criteria this paper constructed an “Illegitimate Scores Checking Scheme” for a scoring method and used the scheme to find out the illegitimate of the current evaluation method of MAT. This paper also proposed a new scoring method that is called the “Standardizing Overall Evaluated Score Method”. This method makes each committee member’s influence tend to be identical. Thus, the committee members can scoring freely according to their partiality without losing the fairness. Finally, it was examined by a large-scale simulation, and the experiment revealed that the it improved the problem of dictatorship and perfectly avoided the situation of cyclical majorities, simultaneously. This result verified that the Standardizing Overall Evaluated Score Method is better than any current evaluation method of MAT.

Keywords: Arrow’s impossibility theorem, most advantageous tender, illegitimate scores checking scheme, standard score.

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Authors: Yang-Wai Chow

Abstract:

This research investigates the design of a low-cost 3D spatial interaction approach using the Wii Remote for immersive Head-Mounted Display (HMD) virtual reality. Current virtual reality applications that incorporate the Wii Remote are either desktop virtual reality applications or systems that use large screen displays. However, the requirements for an HMD virtual reality system differ from such systems. This is mainly because in HMD virtual reality, the display screen does not remain at a fixed location. The user views the virtual environment through display screens that are in front of the user-s eyes and when the user moves his/her head, these screens move as well. This means that the display has to be updated in realtime based on where the user is currently looking. Normal usage of the Wii Remote requires the controller to be pointed in a certain direction, typically towards the display. This is too restrictive for HMD virtual reality systems that ideally require the user to be able to turn around in the virtual environment. Previous work proposed a design to achieve this, however it suffered from a number of drawbacks. The aim of this study is to look into a suitable method of using the Wii Remote for 3D interaction in a space around the user for HMD virtual reality. This paper presents an overview of issues that had to be considered, the system design as well as experimental results.

Keywords: 3D interaction, head-mounted display, virtual reality, Wii remote

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Authors: Shu-Xin Miao

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In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

Keywords: Homotopy perturbation method, fuzzy linear systems, block linear system, fuzzy solution, embedding parameter.

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Authors: P. R. Rahul, A. Kannan

Abstract:

Ultrasound-aided adsorption of phenol by Granular Activated Carbon (GAC) was investigated at different frequencies ranging from 35 kHz, 58 kHz, and 192 kHz. Other factors influencing adsorption such as Adsorbent dosage (g/L), the initial concentration of the phenol solution (ppm) and RPM was also considered along with the frequency variable. However, this study involved calorimetric measurements which helped is determining the effect of frequency on the % removal of phenol from the power dissipated to the system was normalized. It was found that low frequency (35 kHz) cavitation effects had a profound influence on the % removal of phenol per unit power. This study also had cavitation mapping of the ultrasonic baths, and it showed that the effect of cavitation on the adsorption system is irrespective of the position of the vessel. Hence, the vessel was placed at the center of the bath. In this study, novel temperature control and monitoring system to make sure that the system is under proper condition while operations. From the BET studies, it was found that there was only 5% increase in the surface area and hence it was concluded that ultrasound doesn’t profoundly alter the equilibrium value of the adsorption system. DOE studies indicated that adsorbent dosage has a higher influence on the % removal in comparison with other factors.

Keywords: Ultrasound, adsorption, granulated activated carbon, phenol.

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Authors: B. Selma

Abstract:

The aim of this study is to test the feasibility of SIPINA method to predict the harmfulness parameters controlling the seismic response. The approach developed takes into consideration both the focal depth and the peak ground acceleration. The parameter to determine is displacement. The data used for the learning of this method and analysis nonlinear seismic are described and applied to a class of models damaged to some typical structures of the existing urban infrastructure of Jassy, Romania. The results obtained indicate an influence of the focal depth and the peak ground acceleration on the displacement.

Keywords: SIPINA method, seism, focal depth, peak ground acceleration, displacement.

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Authors: Pegah Farshadmanesh, Jamshid Mohammadi, Mehdi Modares

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In nearly all earthquakes of the past century that resulted in moderate to significant damage, the occurrence of postearthquake fire ignition (PEFI) has imposed a serious hazard and caused severe damage, especially in urban areas. In order to reduce the loss of life and property caused by post-earthquake fires, there is a crucial need for predictive models to estimate the PEFI risk. The parameters affecting PEFI risk can be categorized as: 1) factors influencing fire ignition in normal (non-earthquake) condition, including floor area, building category, ignitability, type of appliance, and prevention devices, and 2) earthquake related factors contributing to the PEFI risk, including building vulnerability and earthquake characteristics such as intensity, peak ground acceleration, and peak ground velocity. State-of-the-art statistical PEFI risk models are solely based on limited available earthquake data, and therefore they cannot predict the PEFI risk for areas with insufficient earthquake records since such records are needed in estimating the PEFI model parameters. In this paper, the correlation between normal condition ignition risk, peak ground acceleration, and PEFI risk is examined in an effort to offer a means for predicting post-earthquake ignition events. An illustrative example is presented to demonstrate how such correlation can be employed in a seismic area to predict PEFI hazard.

Keywords: Fire risk, post-earthquake fire ignition (PEFI), risk management, seismicity.

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Authors: Ashish Saini, A.K. Saxena

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The genetic algorithm (GA) based solution techniques are found suitable for optimization because of their ability of simultaneous multidimensional search. Many GA-variants have been tried in the past to solve optimal power flow (OPF), one of the nonlinear problems of electric power system. The issues like convergence speed and accuracy of the optimal solution obtained after number of generations using GA techniques and handling system constraints in OPF are subjects of discussion. The results obtained for GA-Fuzzy OPF on various power systems have shown faster convergence and lesser generation costs as compared to other approaches. This paper presents an enhanced GA-Fuzzy OPF (EGAOPF) using penalty factors to handle line flow constraints and load bus voltage limits for both normal network and contingency case with congestion. In addition to crossover and mutation rate adaptation scheme that adapts crossover and mutation probabilities for each generation based on fitness values of previous generations, a block swap operator is also incorporated in proposed EGA-OPF. The line flow limits and load bus voltage magnitude limits are handled by incorporating line overflow and load voltage penalty factors respectively in each chromosome fitness function. The effects of different penalty factors settings are also analyzed under contingent state.

Keywords: Contingent operation state, Fuzzy rule base, Genetic Algorithms, Optimal Power Flow.

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Authors: Mehrdad N. Khajavi, Bahram Notghi, Golamhassan Paygane

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Vehicle suspension design must fulfill some conflicting criteria. Among those is ride comfort which is attained by minimizing the acceleration transmitted to the sprung mass, via suspension spring and damper. Also good handling of a vehicle is a desirable property which requires stiff suspension and therefore is in contrast with a vehicle with good ride. Among the other desirable features of a suspension is the minimization of the maximum travel of suspension. This travel which is called suspension working space in vehicle dynamics literature is also a design constraint and it favors good ride. In this research a full car 8 degrees of freedom model has been developed and the three above mentioned criteria, namely: ride, handling and working space has been adopted as objective functions. The Multi Objective Programming (MOP) discipline has been used to find the Pareto Front and some reasoning used to chose a design point between these non dominated points of Pareto Front.

Keywords: Vehicle, Ride, Handling, Suspension, Working Space, Multi Objective Programming.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

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The necessity of solving multi dimensional complicated scientific problems beside the necessity of several objective functions optimization are the most motive reason of born of artificial intelligence and heuristic methods. In this paper, we introduce a new method for multiobjective optimization based on learning automata. In the proposed method, search space divides into separate hyper-cubes and each cube is considered as an action. After gathering of all objective functions with separate weights, the cumulative function is considered as the fitness function. By the application of all the cubes to the cumulative function, we calculate the amount of amplification of each action and the algorithm continues its way to find the best solutions. In this Method, a lateral memory is used to gather the significant points of each iteration of the algorithm. Finally, by considering the domination factor, pareto front is estimated. Results of several experiments show the effectiveness of this method in comparison with genetic algorithm based method.

Keywords: Function optimization, Multiobjective optimization, Learning automata.

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Authors: P.Varzakas

Abstract:

In this paper, an accurate theoretical analysis for the achievable average channel capacity (in the Shannon sense) per user of a hybrid cellular direct-sequence/fast frequency hopping code-division multiple-access (DS/FFH-CDMA) system operating in a Rayleigh fading environment is presented. The analysis covers the downlink operation and leads to the derivation of an exact mathematical expression between the normalized average channel capacity available to each system-s user, under simultaneous optimal power and rate adaptation and the system-s parameters, as the number of hops per bit, the processing gain applied, the number of users per cell and the received signal-tonoise power ratio over the signal bandwidth. Finally, numerical results are presented to illustrate the proposed mathematical analysis.

Keywords: Shannon capacity, adaptive systems, code-division multiple access, fading channels.

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Authors: N. Q. Bau, N. V. Nghia

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The acoustomagnetoelectric (AME) field in a rectangular quantum wire with an infinite potential (RQWIP) is calculated in the presence of an external magnetic field (EMF) by using the quantum kinetic equation for the distribution function of electrons system interacting with external phonons and electrons scattering with internal acoustic phonon in a RQWIP. We obtained ananalytic expression for the AME field in the RQWIP in the presence of the EMF. The dependence of AME field on the frequency of external acoustic wave, the temperature T of system, the cyclotron frequency of the EMF and the intensity of the EMF is obtained. Theoretical results for the AME field are numerically evaluated, plotted and discussed for a specific RQWIP GaAs/GaAsAl. This result has shown that the dependence of the AME field on intensity of the EMF is nonlinearly and it is many distinct maxima in the quantized magnetic region. We also compared received fields with those for normal bulk semiconductors, quantum well and quantum wire to show the difference. The influence of an EMF on AME field in a RQWIP is newly developed.

Keywords: Rectangular quantum wire, acoustomagnetoelectric field, electron-phonon interaction, kinetic equation method.

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Authors: Oh-Yeol Kwon, Sung-Il Chien

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A conventional image posterization method occasionally fails to preserve the shape and color of objects due to the uneffective color reduction. This paper proposes a new image posterizartion method by using modified color quantization for preserving the shape and color of objects and color contrast enhancement for improving lightness contrast and saturation. Experiment results show that our proposed method can provide visually more satisfactory posterization result than that of the conventional method.

Keywords: Color contrast enhancement, color quantization, color segmentation, image posterization

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Authors: Deeman Yousif Mahmood, Mohammed Abdullah Hussein

Abstract:

The goal of a network-based intrusion detection system is to classify activities of network traffics into two major categories: normal and attack (intrusive) activities. Nowadays, data mining and machine learning plays an important role in many sciences; including intrusion detection system (IDS) using both supervised and unsupervised techniques. However, one of the essential steps of data mining is feature selection that helps in improving the efficiency, performance and prediction rate of proposed approach. This paper applies unsupervised K-means clustering algorithm with information gain (IG) for feature selection and reduction to build a network intrusion detection system. For our experimental analysis, we have used the new NSL-KDD dataset, which is a modified dataset for KDDCup 1999 intrusion detection benchmark dataset. With a split of 60.0% for the training set and the remainder for the testing set, a 2 class classifications have been implemented (Normal, Attack). Weka framework which is a java based open source software consists of a collection of machine learning algorithms for data mining tasks has been used in the testing process. The experimental results show that the proposed approach is very accurate with low false positive rate and high true positive rate and it takes less learning time in comparison with using the full features of the dataset with the same algorithm.

Keywords: Information Gain (IG), Intrusion Detection System (IDS), K-means Clustering, Weka.

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Authors: Peng Li, Chuanri Li, Tao Li

Abstract:

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method, and gives concrete processes on determining the factor and sub-factor sets, weight sets, judgment set, and multi-stage fuzzy evaluation. To determine the weight of factor and sub-factor sets, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: Reliability allocation, fuzzy arithmetic, allocation weight.

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Authors: Ayad Salih Sabbar, Amin Chegenizadeh, Hamid Nikraz

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Utilizing waste materials in civil engineering applications has a positive influence on the environment by reducing carbon dioxide emissions and issues associated with waste disposal. Granulated blast furnace slag (GBFS) is a by-product of the iron and steel industry, with millions of tons of slag being annually produced worldwide. Slag has been widely used in structural engineering and for stabilizing clay soils; however, studies on the effect of slag on sandy soils are scarce. This article investigates the effect of slag content on shear strength parameters through direct shear tests and unconsolidated undrained triaxial tests on mixtures of Perth sand and slag. For this purpose, sand-slag mixtures, with slag contents of 2%, 4%, and 6% by weight of samples, were tested with direct shear tests under three normal stress values, namely 100 kPa, 150 kPa, and 200 kPa. Unconsolidated undrained triaxial tests were performed under a single confining pressure of 100 kPa and relative density of 80%. The internal friction angles and shear stresses of the mixtures were determined via the direct shear tests, demonstrating that shear stresses increased with increasing normal stress and the internal friction angles and cohesion increased with increasing slag. There were no significant differences in shear stresses parameters when slag content rose from 4% to 6%. The unconsolidated undrained triaxial tests demonstrated that shear strength increased with increasing slag content.

Keywords: Direct shear, shear strength, slag, UU test.

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Jeff Clarine, Chang-Shyh Peng, Daisy Sang

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Bioassay is the measurement of the potency of a chemical substance by its effect on a living animal or plant tissue. Bioassay data and chemical structures from pharmacokinetic and drug metabolism screening are mined from and housed in multiple databases. Bioassay prediction is calculated accordingly to determine further advancement. This paper proposes a four-step preprocessing of datasets for improving the bioassay predictions. The first step is instance selection in which dataset is categorized into training, testing, and validation sets. The second step is discretization that partitions the data in consideration of accuracy vs. precision. The third step is normalization where data are normalized between 0 and 1 for subsequent machine learning processing. The fourth step is feature selection where key chemical properties and attributes are generated. The streamlined results are then analyzed for the prediction of effectiveness by various machine learning algorithms including Pipeline Pilot, R, Weka, and Excel. Experiments and evaluations reveal the effectiveness of various combination of preprocessing steps and machine learning algorithms in more consistent and accurate prediction.

Keywords: Bioassay, machine learning, preprocessing, virtual screen.

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Authors: Mahmoud Zarrini, Sanaz Torkaman

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In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

Keywords: Fuzzy Fredholm Integral Equation, Bernstein, Block-Pulse, Orthonormal.

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Authors: Eric Huang, Coleman DeLude, Justin Romberg, Saibal Mukhopadhyay, Madhavan Swaminathan

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High-performance computing (HPC) based emulators can be used to model the scattering from multiple stationary and moving targets for RADAR applications. These emulators rely on the RADAR Cross Section (RCS) of the targets being available in complex scenarios. Representing the RCS using tables generated from EM simulations is oftentimes cumbersome leading to large storage requirements. In this paper, we proposed a spherical harmonic based anisotropic scatterer model to represent the RCS of complex targets. The problem of finding the locations and reflection profiles of all scatterers can be formulated as a linear least square problem with a special sparsity constraint. We solve this problem using a modified Orthogonal Matching Pursuit algorithm. The results show that the spherical harmonic based scatterer model can effectively represent the RCS data of complex targets.

Keywords: RADAR, RCS, high performance computing, point scatterer model

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Authors: Robert Setekera, Luuk Tiemeijer, Ramses van der Toorn

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In this paper an extensive verification of the extraction method (published earlier) that consistently accounts for self-heating and Early effect to accurately extract both base and thermal resistance of bipolar junction transistors is presented. The method verification is demonstrated on advanced RF SiGe HBTs were the extracted results for the thermal resistance are compared with those from another published method that ignores the effect of Early effect on internal base-emitter voltage and the extracted results of the base resistance are compared with those determined from noise measurements. A self-consistency of our method in the extracted base resistance and thermal resistance using compact model simulation results is also carried out in order to study the level of accuracy of the method.

Keywords: Avalanche, Base resistance, Bipolar transistor, Compact modeling, Early voltage, Thermal resistance, Self-heating, parameter extraction.

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Authors: Seong-Bae Park, Hee-Geun Yoon

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It is an important task in Korean-English machine translation to classify the gender of names correctly. When a sentence is composed of two or more clauses and only one subject is given as a proper noun, it is important to find the gender of the proper noun for correct translation of the sentence. This is because a singular pronoun has a gender in English while it does not in Korean. Thus, in Korean-English machine translation, the gender of a proper noun should be determined. More generally, this task can be expanded into the classification of the general Korean names. This paper proposes a statistical method for this problem. By considering a name as just a sequence of syllables, it is possible to get a statistics for each name from a collection of names. An evaluation of the proposed method yields the improvement in accuracy over the simple looking-up of the collection. While the accuracy of the looking-up method is 64.11%, that of the proposed method is 81.49%. This implies that the proposed method is more plausible for the gender classification of the Korean names.

Keywords: machine translation, natural language processing, gender of proper nouns, statistical method

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Authors: Mehdi Tatari

Abstract:

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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Authors: V. R. Ahire, A. Kumar, B. N. Pandey, K. P. Mishra, G. R. Kulkarni

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Radiation therapy is an effective vital strategy used globally in the treatment of cervical cancer. However, radiation efficacy principally depends on the radiosensitivity of the tumor, and not all patient exhibit significant response to irradiation. A radiosensitive tumor is easier to cure than a radioresistant tumor which later advances to local recurrence and metastasis. Herbal polyphenols are gaining attention for exhibiting radiosensitization through various signaling. Current work focuses to study the radiosensitization effect of ellagic acid (EA), on HeLa cells. EA intermediated radiosensitization of HeLa cells was due to the induction γ-H2AX foci formation, G1 phase cell cycle arrest, and loss of reproductive potential, growth inhibition, drop in the mitochondrial membrane potential and protein expression studies that eventually induced apoptosis. Irradiation of HeLa in presence of EA (10 μM) to doses of 2 and 4 Gy γ-radiation produced marked tumor cytotoxicity. EA also demonstrated radio-protective effect on normal cell, NIH3T3 and aided recovery from the radiation damage. Our results advocate EA to be an effective adjuvant for improving cancer radiotherapy as it displays striking tumor cytotoxicity and reduced normal cell damage instigated by irradiation.

Keywords: Apoptotic radiosensitivity, ellagic acid, mitochondrial potential, cell-cycle arrest.

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Authors: Evangelos G. Karvelas, Christos Liosis, Andreas Theodorakakos, Theodoros E. Karakasidis

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In the present work, a numerical method for the estimation of the appropriate gradient magnetic fields for optimum driving of the particles into the desired area inside the human body is presented. The proposed method combines Computational Fluid Dynamics (CFD), Discrete Element Method (DEM) and Covariance Matrix Adaptation (CMA) evolution strategy for the magnetic navigation of nanoparticles. It is based on an iteration procedure that intents to eliminate the deviation of the nanoparticles from a desired path. Hence, the gradient magnetic field is constantly adjusted in a suitable way so that the particles’ follow as close as possible to a desired trajectory. Using the proposed method, it is obvious that the diameter of particles is crucial parameter for an efficient navigation. In addition, increase of particles' diameter decreases their deviation from the desired path. Moreover, the navigation method can navigate nanoparticles into the desired areas with efficiency approximately 99%.

Keywords: CFD, CMA evolution strategy, DEM, magnetic navigation, spherical particles.

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Authors: Muhammad Rana, Quazi Mamun, Rafiqul Islam

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In the Internet of Things (IoT), many devices are connected and accumulate a sheer amount of data. These Internet-driven raw data need to be transferred securely to the end-users via dependable networks. Consequently, the challenges of IoT security in various IoT domains are paramount. Cryptography is being applied to secure the networks for authentication, confidentiality, data integrity and access control. However, due to the resource constraint properties of IoT devices, the conventional cipher may not be suitable in all IoT networks. This paper designs a robust and effective lightweight cipher to secure the IoT environment and meet the resource-constrained nature of IoT devices. We also propose a symmetric and block-cipher based lightweight cryptographic algorithm. The proposed algorithm increases the complexity of the block cipher, maintaining the lowest computational requirements possible. The proposed algorithm efficiently constructs the key register updating technique, reduces the number of encryption rounds, and adds a layer between the encryption and decryption processes.

Keywords: Internet of Things, IoT, cryptography block cipher, s-box, key management, IoT security.

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Authors: Felix Baumann, Aleksandar Milutinovic, Dieter Roller

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Up to this point business process management projects in general and business process modelling projects in particular could not rely on a practical and scientifically validated method to estimate cost and effort. Especially the model development phase is not covered by a cost estimation method or model. Further phases of business process modelling starting with implementation are covered by initial solutions which are discussed in the literature. This article proposes a method of filling this gap by deriving a cost estimation method from available methods in similar domains namely software development or software engineering. Software development is regarded as closely similar to process modelling as we show. After the proposition of this method different ideas for further analysis and validation of the method are proposed. We derive this method from COCOMO II and Function Point which are established methods of effort estimation in the domain of software development. For this we lay out similarities of the software development process and the process of process modelling which is a phase of the Business Process Management life-cycle.

Keywords: Cost Estimation, Effort Estimation, Process Modelling, Business Process Management, COCOMO.

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

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By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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