Search results for: iteration procedure

Authors: Kholod Mohammad Abualnaja

Abstract:

A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Yixun Shi

Abstract:

Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

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Authors: Olayiwola Moruf Oyedunsi

Abstract:

This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: M. O. Olayiwola

Abstract:

Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

Abstract:

Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Alemayehu Geremew Geremew

Abstract:

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Taysir Soliman

Abstract:

One of the current popular clustering techniques is Spectral Clustering (SC) because of its advantages over conventional approaches such as hierarchical clustering, k-means, etc. and other techniques as well. However, one of the disadvantages of SC is the time consuming process because it requires computing the eigenvectors. In the past to overcome this disadvantage, a number of attempts have been proposed such as the Power Iteration Clustering (PIC) technique, which is one of versions from SC; some of PIC advantages are: 1) its scalability and efficiency, 2) finding one pseudo-eigenvectors instead of computing eigenvectors, and 3) linear combination of the eigenvectors in linear time. However, its worst disadvantage is an inter-class collision problem because it used only one pseudo-eigenvectors which is not enough. Previous researchers developed Deflation-based Power Iteration Clustering (DPIC) to overcome problems of PIC technique on inter-class collision with the same efficiency of PIC. In this paper, we developed Parallel DPIC (PDPIC) to improve the time and memory complexity which is run on apache spark framework using sparse matrix. To test the performance of PDPIC, we compared it to SC, ESCG, ESCALG algorithms on four small graph benchmark datasets and nine large graph benchmark datasets, where PDPIC proved higher accuracy and better time consuming than other compared algorithms.

Keywords: spectral clustering, power iteration clustering, deflation-based power iteration clustering, Apache spark, large graph

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Authors: Guenther Schuh, Michael Riesener, Jan Kantelberg

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Due to the fugacity of markets and the reduction of product lifecycles, manufacturing companies from high-wage countries are nowadays faced with the challenge to place more innovative products within even shorter development time on the market. At the same time, volatile customer requirements have to be satisfied in order to successfully differentiate from market competitors. One potential approach to address the explained challenges is provided by agile values and principles. These agile values and principles already proofed their success within software development projects in the form of management frameworks like Scrum or concrete procedure models such as Extreme Programming or Crystal Clear. Those models lead to significant improvements regarding quality, costs and development time and are therefore used within most software development projects. Motivated by the success within the software industry, manufacturing companies have tried to transfer agile mechanisms of action to the development of hardware products ever since. Though first empirical studies show similar effects in the agile development of hardware products, no comprehensive procedure model for the design of development iterations has been developed for hardware development yet due to different constraints of the domains. For this reason, this paper focusses on the design of agile product development processes by transferring mechanisms of action used in agile software development towards product development. This is conducted by decomposing the individual systems 'product development' and 'agile software development' into relevant elements and symbiotically composing the elements of both systems in respect of the design of agile product development processes afterwards. In a first step, existing product development processes are described following existing approaches of the system theory. By analyzing existing case studies from industrial companies as well as academic approaches, characteristic objectives, activities and artefacts are identified within a target-, action- and object-system. In partial model two, mechanisms of action are derived from existing procedure models of agile software development. These mechanisms of action are classified in a superior strategy level, in a system level comprising characteristic, domain-independent activities and their cause-effect relationships as well as in an activity-based element level. Within partial model three, the influence of the identified agile mechanism of action towards the characteristic system elements of product development processes is analyzed. For this reason, target-, action- and object-system of the product development are compared with the strategy-, system- and element-level of agile mechanism of action by using the graph theory. Furthermore, the necessity of existence of activities within iteration can be determined by defining activity-specific degrees of freedom. Based on this analysis, agile product development processes are designed in form of different types of iterations within a last step. By defining iteration-differentiating characteristics and their interdependencies, a logic for the configuration of activities, their form of execution as well as relevant artefacts for the specific iteration is developed. Furthermore, characteristic types of iteration for the agile product development are identified.

Keywords: activity-based process model, agile mechanisms of action, agile product development, degrees of freedom

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

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In this paper, first, we propose least support orthogonal matching pursuit (LS-OMP) algorithm to improve the performance, of the OMP (orthogonal matching pursuit) algorithm. LS-OMP algorithm adaptively chooses optimum L (least part of support), at each iteration. This modification helps to reduce the computational complexity significantly and performs better than OMP algorithm. Second, we give the procedure for the invisible image watermarking in the presence of compressive sampling. The image reconstruction based on a set of watermarked measurements is performed using LS-OMP.

Keywords: compressed sensing, orthogonal matching pursuit, restricted isometry property, signal reconstruction, least support orthogonal matching pursuit, watermark

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Tahir Mehmood, Pennung Warnitchai

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Simplified static analysis procedures such Nonlinear Static Procedure (NSP) are gaining popularity for the seismic evaluation of buildings. However, these simplified procedures accounts only for the seismic responses of the fundamental vibration mode of the structure. Some other procedures which can take into account the higher modes of vibration, lack in accuracy to determine the component responses. Hence, such procedures are not suitable for evaluating the structures where many vibration modes may participate significantly or where component responses are needed to be evaluated. Moreover, these procedures were found to either computationally expensive or tedious to obtain individual component responses. In this paper, a simplified but accurate procedure is studied. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. In this procedure, the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The responses of four tall buildings are computed by this simplified UMRHA procedure and compared with those obtained from the NLRHA procedure. The comparison shows that the UMRHA procedure is able to accurately compute the global responses, i.e., story shears and story overturning moments, floor accelerations and inter-story drifts as well as the component level responses of these tall buildings with heights varying from 20 to 44 stories. The required computational effort is also extremely low compared to that of the Nonlinear Response History Analysis (NLRHA) procedure.

Keywords: higher mode effects, seismic evaluation procedure, tall buildings, component responses

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Mamta Thakur, Dr. Shashi Mawar, Ms. Levis Murry, Dr. D.k.sharma

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Aim: The aim of this study is to develop nephrology nursing procedure protocol after clinical audit of current nephrology nursing practices. Materials and methods: This descriptive observational study was conducted on 40 nurses who were working in Nephrology Department of AIIMS, New Delhi to observe their current practices to assess the existing gaps in the practice. The nurses were enrolled through total enumerative sampling. Sociodemographic profile of nurses and clinical profile for site of procedure was collected. Observation checklist was formed on the basis of standard nursing practices, which included 7 dimensions for hemodialysis procedure and 3 dimensions for procedure of assisting renal biopsy. Based on the gaps identified, nephrology nursing procedure protocol will be developed. Nurses were observed during two shifts, and each nurse was observed once. Scoring of items were done in each dimension, and for acceptable practices, nurses have to score ≥80% in each dimension. Results: Data was analyzed using descriptive statistics. Majority of nurses (73.7%) in nephrology ward and (80.9%) in hemodialysis unit have not undergone any special training in nephrology. Most of nurses (80.9%) followed the acceptable nursing practices for procedure of connection for hemodialysis. None of nurses followed the acceptable level (≥80%) of nursing practices for the procedure of predialysis assessment, the procedure for site preparation, during dialysis assessment and post dialysis assessment. None (100%) showed the acceptable level of nursing practices for all the dimensions of assisting renal biopsy procedure. Nephrology nursing procedure protocol was developed by researcher following a rigorous process, and this will reduce the gaps in the nursing practice. Conclusion: Clinical audit found that there were gaps in the existing nursing practices compared to the standardised nursing practices for procedure of hemodialysis and assisting renal biopsy, and these gaps have been addressed by the development of the protocol.

Keywords: nursing practice, nephrology nursing procedure, nursing protocol, renal biopsy, hemodialysis

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Authors: Wided Batita, Stéphane Roche, Claude Caron

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Geodesign is an emergent term related to a new and complex process. Hence, it needs to rethink tools, technologies and platforms in order to efficiently achieve its goals. A few tools have emerged since 2010 such as CommunityViz, GeoPlanner, etc. In the era of Web 2.0 and collaboration, WikiGIS has been proposed as a new category of tools. In this paper, we present WikiGIS functionalities dealing mainly with the iteration and traceability management to support the collaboration of the Geodesign process. Actually, WikiGIS is built on GeoWeb 2.0 technologies —and primarily on wiki— and aims at managing the tracking of participants’ editing. This paper focuses on a simplified simulation to illustrate the strength of WikiGIS in the management of traceability and in the access to history in a Geodesign process. Indeed, a cartographic user interface has been implemented, and then a hypothetical use case has been imagined as proof of concept.

Keywords: geodesign, history, traceability, tracking of participants’ editing, WikiGIS

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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: Aigin Bashti

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Preparation of multicomponent reactions (MCRs) via a simple one-pot strategy is considered a novel procedure which has attracted a lot of interest from organic and medicinal chemists. Due to the great importance of phthalazide triones, it was decided to introduce a novel and cost-effective green procedure for the preparation of these derivatives. In this methodology, an efficient 4,4ʹ-Bipyridinium Dichloride Ordered Mesoporous Silica functionalized catalyst (BP-SBA-15) was utilized. The catalyst was characterized by X-ray diffraction analysis (XRD), field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), thermo-gravimetric analysis (TGA), and Fourier-transform infrared spectroscopy (FT-IR) analysis. In conclusion, it should be mentioned that this methodology has some advantages, including short reaction time, high yield of the products, recyclable catalyst, green procedure, and facile work-up procedure. The catalyst was successfully utilized for the one-pot preparation of various phthalazinetrione derivatives.

Keywords: dimedone, green procedure, multicomponent reactions, phthalhydrazide

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Authors: E. L. Elghazy, A. M. Sanad, M. G. Ghoneim

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Over the past two decades research has shown that fiber reinforced polymers can be efficiently, economically and safely used for strengthening and rehabilitation of reinforced concrete (RC) structures. Designing FRP confined concrete columns requires reliable analytical tools that predict the level of performance and ductility enhancement. A numerical procedure is developed aiming at determining the type and thickness of FRP jacket needed to achieve a certain level of ductility enhancement. The procedure starts with defining the stress strain curve, which is used to obtain moment curvature relationship then displacement ductility ratio of reinforced concrete cross-sections subjected to bending moment and axial force. Three sets of published experimental tests were used to validate the numerical procedure. Comparisons between predicted results obtained by using the proposed procedure and actual results of experimental tests proved the reliability of the proposed procedure.

Keywords: columns, confinement, ductility, FRP, numerical

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Authors: Jirawan Jitthavech, Vichit Lorchirachoonkul

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A statistical procedure using multiple comparisons test for proportions is proposed for variable selection in a data envelopment analysis (DEA) model. The test statistic in the multiple comparisons is the proportion of efficient decision making units (DMUs) in a DEA model. Three methods of multiple comparisons test for proportions: multiple Z tests with Bonferroni correction, multiple tests in 2Xc crosstabulation and the Marascuilo procedure, are used in the proposed statistical procedure of iteratively eliminating the variables in a backward manner. Two simulation populations of moderately and lowly correlated variables are used to compare the results of the statistical procedure using three methods of multiple comparisons test for proportions with the hypothesis testing of the efficiency contribution measure. From the simulation results, it can be concluded that the proposed statistical procedure using multiple Z tests for proportions with Bonferroni correction clearly outperforms the proposed statistical procedure using the remaining two methods of multiple comparisons and the hypothesis testing of the efficiency contribution measure.

Keywords: Bonferroni correction, efficient DMUs, Marascuilo procedure, Pastor et al. method, 2xc crosstabulation

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Authors: David C. Ni

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In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Alldila Hendy, Agi Satria

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Background: A colostomy procedure is an important part in the management of surgical procedures in some diseases involving the gastrointestinal tract. So it is necessary to find the factors that influence the occurrence of complications. Methods: This is a retrospective cross-sectional analytic study in Cipto Mangunkusumo Hospital noting medical records of patients after the colostomy from January 2012 to December 2014 at the Division of Digestive Surgery. Results: In 136 cases of post-colostomy, 66 cases have complications, 14 is early-onset, and 52 is late-onset. 70 is without complications. Most complications are dermatitis, which is 31 (22.8%), cases of infection/abscess/fistula and intestinal obstruction are 13 (9.6%) and 5 patients (4.4%). A rare complication is colostomy retraction by 2 patients (1.5%), colostomy prolapse and necrosis/gangrene, which is only 3 patients (2.2%). A colostomy procedure in emergency surgery is riskier than elective surgery for complications after colostomy (p < 0.007, OR 2.85), Based on the operator who performs a colostomy procedure, the consultant had a lower risk of complications than fellow or resident (p < 0.0001). Based on the age factor, where the age of about 50 years has a risk of complications after colostomy (p < 0.018). Conclusion: The timing of operation (emergency or elective), age, and operator who perform a colostomy procedure have a significant relationship with an increased prevalence of complications after colostomy in RSCM.

Keywords: colostomy, complications, factors, procedure

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Authors: Sanjay Rathee, Arti Kashyap

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Extraction of useful information from large datasets is one of the most important research problems. Association rule mining is one of the best methods for this purpose. Finding possible associations between items in large transaction based datasets (finding frequent patterns) is most important part of the association rule mining. There exist many algorithms to find frequent patterns but Apriori algorithm always remains a preferred choice due to its ease of implementation and natural tendency to be parallelized. Many single-machine based Apriori variants exist but massive amount of data available these days is above capacity of a single machine. Therefore, to meet the demands of this ever-growing huge data, there is a need of multiple machines based Apriori algorithm. For these types of distributed applications, MapReduce is a popular fault-tolerant framework. Hadoop is one of the best open-source software frameworks with MapReduce approach for distributed storage and distributed processing of huge datasets using clusters built from commodity hardware. However, heavy disk I/O operation at each iteration of a highly iterative algorithm like Apriori makes Hadoop inefficient. A number of MapReduce-based platforms are being developed for parallel computing in recent years. Among them, two platforms, namely, Spark and Flink have attracted a lot of attention because of their inbuilt support to distributed computations. Earlier we proposed a reduced- Apriori algorithm on Spark platform which outperforms parallel Apriori, one because of use of Spark and secondly because of the improvement we proposed in standard Apriori. Therefore, this work is a natural sequel of our work and targets on implementing, testing and benchmarking Apriori and Reduced-Apriori and our new algorithm ReducedAll-Apriori on Apache Flink and compares it with Spark implementation. Flink, a streaming dataflow engine, overcomes disk I/O bottlenecks in MapReduce, providing an ideal platform for distributed Apriori. Flink's pipelining based structure allows starting a next iteration as soon as partial results of earlier iteration are available. Therefore, there is no need to wait for all reducers result to start a next iteration. We conduct in-depth experiments to gain insight into the effectiveness, efficiency and scalability of the Apriori and RA-Apriori algorithm on Flink.

Keywords: apriori, apache flink, Mapreduce, spark, Hadoop, R-Apriori, frequent itemset mining

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Authors: L. Hamra, J. F. Demonceau, V. Denoël

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The aim of this paper is to study a beam extracted from a frame and subjected to blast loading. The demand of ductility depends on six dimensionless parameters: two related to the blast loading, two referring to the bending behavior of the beam and two corresponding to the dynamic behavior of the rest of the structure. We develop a full analytical procedure that provides the ductility demand as a function of these six dimensionless parameters.

Keywords: analytical procedure, blast loading, membrane force, P-I diagram

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Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon

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In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.

Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation

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Authors: Hong Lu, Xiong Xiao

Abstract:

Shaft parts are widely used in machinery industry, however, bending deformation often occurred when this kind of parts is being heat treated. This parts needs to be straightened to meet the requirement of straightness. As for the pressure straightening process, a good straightening stroke algorithm is related to the precision and efficiency of straightening process. In this paper, the relationship between straightening load and deflection during the straightening process is analyzed, and the mathematical model of the straightening process has been established. By the mathematical model, the iterative method is used to solve the straightening stroke. Compared to the traditional straightening stroke algorithm, straightening stroke calculated by this method is much more precise; because it can adapt to the change of material performance parameters. Considering that the straightening method is widely used in the mass production of the shaft parts, knowledge base is used to store the data of the straightening process, and a straightening stroke algorithm based on empirical data is set up. In this paper, the straightening process control model which combine the straightening stroke method based on iteration and straightening stroke algorithm based on empirical data has been set up. Finally, an experiment has been designed to verify the straightening process control model.

Keywords: straightness, straightening stroke, deflection, shaft parts

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Authors: Shunpu Zhang

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We propose a new multiple test called the minPOP test for testing multiple hypotheses simultaneously. Under the assumption that the test statistics are independent, we show that the minPOP test has higher global power than the existing multiple testing methods. We further propose a stepwise multiple-testing procedure based on the minPOP test and two of its modified versions (the Double Truncated and Left Truncated minPOP tests). We show that these multiple tests have strong control of the family-wise error rate (FWER). A method for finding the p-values of the proposed tests after adjusting for multiplicity is also developed. Simulation results show that the Double Truncated and Left Truncated minPOP tests, in general, have a higher number of rejections than the existing multiple testing procedures.

Keywords: multiple test, single-step procedure, stepwise procedure, p-value for multiple testing

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