Search results for: Model Order Reduction

Authors: Ondruska Marek, Matustik Ondrej

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The main goal of the article is to present new model of application architecture of banking IT solution providing the Internet Banking services that is particularly outsourced. At first, we propose business rationale and a SWOT analysis to explain the reasons for the model in the article. The most important factor for our model is nowadays- big boom around smart phones and tablet devices. As next, we focus on IT architecture viewpoint where we design application, integration and security model. Finally, we propose a generic governance model that serves as a basis for the specialized governance model. The specialized instance of governance model is designed to ensure that the development and the maintenance of different parts of the IT solution are well governed in time.

Keywords: governance model, front-end application, Internet Banking, smart phones

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Authors: G. Tamulevičius, A. Serackis, T. Sledevič, D. Navakauskas

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We consider the biggest challenge in speech recognition – noise reduction. Traditionally detected transient noise pulses are removed with the corrupted speech using pulse models. In this paper we propose to cope with the problem directly in Dynamic Time Warping domain. Bidirectional Dynamic Time Warping algorithm for the recognition of isolated words impacted by transient noise pulses is proposed. It uses simple transient noise pulse detector, employs bidirectional computation of dynamic time warping and directly manipulates with warping results. Experimental investigation with several alternative solutions confirms effectiveness of the proposed algorithm in the reduction of impact of noise on recognition process – 3.9% increase of the noisy speech recognition is achieved.

Keywords: Transient noise pulses, noise reduction, dynamic time warping, speech recognition.

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Authors: Jin-Tae Lee, Jung-Hoon Suh, Sang-Soo Jang, Jae-Il Lee

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Information and communication service providers (ICSP) that are significant in size and provide Internet-based services take administrative, technical, and physical protection measures via the information security check service (ISCS). These protection measures are the minimum action necessary to secure the stability and continuity of the information and communication services (ICS) that they provide. Thus, information assets are essential to providing ICS, and deciding the relative importance of target assets for protection is a critical procedure. The risk analysis model designed to decide the relative importance of information assets, which is described in this study, evaluates information assets from many angles, in order to choose which ones should be given priority when it comes to protection. Many-sided risk analysis (MSRS) grades the importance of information assets, based on evaluation of major security check items, evaluation of the dependency on the information and communication facility (ICF) and influence on potential incidents, and evaluation of major items according to their service classification, in order to identify the ISCS target. MSRS could be an efficient risk analysis model to help ICSPs to identify their core information assets and take information protection measures first, so that stability of the ICS can be ensured.

Keywords: Information Asset, Information CommunicationFacility, Evaluation, ISCS (Information Security Check Service), Evaluation, Grade.

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Authors: Le Kang

Abstract:

According to the nature of the university, as a free and responsible academic community, USR is based on a different foundation —academic responsibility, so the Pyramid and the IC Model of CSR could not fully explain the most distinguished feature of USR. This paper sought to put forward a new model— Ferris Wheel Model, to illustrate the nature of USR and the process of achievement. The Ferris Wheel Model of USR shows the university creates a balanced, fairness and neutrality systemic structure to afford social responsibilities; that makes the organization could obtain a synergistic effect to achieve more extensive interests of stakeholders and wider social responsibilities.

Keywords: USR, Achievement model, Ferris wheel model.

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Authors: M. Tahar Bouzaher

Abstract:

This study involves a numerical simulation of the flow around a NACA2415 airfoil, with a 15°angle of attack, and flow separation control using a rod, It reposes inputting a cylindrical rod upstream of the leading edge in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The viscous, non-stationary flow is simulated using ANSYS FLUENT 13. Our results showed a substantial modification in the flow behavior and a maximum drag reduction of 51%.

Keywords: CFD, Flow separation, Active control, Boundary layer, rod, NACA 2415.

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Authors: Maziyar Nouraee

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Electronic markets in recent decades contribute remarkably in business transactions. Many organizations consider traditional ways of trade non-economical and therefore they do trade only through electronic markets. There are different categorizations of electronic markets functions. In one classification, functions of electronic markets are categorized into classes as information, transactions, and value added. In the present paper, effects of the three classes on the two major elements of the supply chain management are measured. The two elements are decrease in the product unit cost and reduction in response time to the customer. The results of the current research show that among nine minor elements related to the three classes of electronic markets functions, six factors and three factors influence on reduction of the product unit cost and reduction of response time to the customer, respectively.

Keywords: Electronic Commerce, Electronic Market, B2B Trade, Supply Chain Management.

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Authors: Megumi Shibuya, Tomohiko Ogishi

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Recently, content delivery services have grown rapidly over the Internet. For ASPs (Application Service Provider) providing content delivery services, P2P architecture is beneficial to reduce outgoing traffic from content servers. On the other hand, ISPs are suffering from the increase in P2P traffic. The P2P traffic is unnecessarily redundant because the same content or the same fractions of content are transferred through an inter-ISP link several times. Subscriber ISPs have to pay a transit fee to upstream ISPs based on the volume of inter-ISP traffic. In order to solve such problems, several works have been done for the purpose of P2P traffic reduction. However, these existing works cannot control the traffic volume of a certain link. In order to solve such an ISP-s operational requirement, we propose a method to control traffic volume for a link within a preconfigured upper bound value. We evaluated that the proposed method works well by conducting a simulation on a 1,000-user scale. We confirm that the traffic volume could be controlled at a lower level than the upper bound for all evaluated conditions. Moreover, our method could control the traffic volume at 98.95% link usage against the target value.

Keywords: P2P, traffic control, traffic localization, ALTO.

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Authors: Hee-Chang Lim

Abstract:

The study aims to understand the surface pressure distribution around the bodies such as the suction pressure in the leading edge on the top and side-face when the aspect ratio of bodies and the wind direction are changed, respectively. We carried out the wind tunnel measurement and numerical simulation around a series of rectangular bodies (40^d×80^w×80^h, 80^d×80^w×80^h, 160^d×80^w×80^h, 80^d×40^w×80^h and 80^d×160^w×80^h in mm³) placed in a deep turbulent boundary layer. Based on a modern numerical platform, the Navier-Stokes equation with the typical 2-equation (k-ε model) and the DES (Detached Eddy Simulation) turbulence model has been calculated, and they are both compared with the measurement data. Regarding the turbulence model, the DES model makes a better prediction comparing with the k-ε model, especially when calculating the separated turbulent flow around a bluff body with sharp edged corner. In order to observe the effect of wind direction on the pressure variation around the cube (e.g., 80^d×80^w×80^h in mm), it rotates at 0º, 10º, 20º, 30º, and 45º, which stands for the salient wind directions in the tunnel. The result shows that the surface pressure variation is highly dependent upon the approaching wind direction, especially on the top and the side-face of the cube. In addition, the transverse width has a substantial effect on the variation of surface pressure around the bodies, while the longitudinal length has little or no influence.

Keywords: Rectangular bodies, wind direction, aspect ratio, surface pressure distribution, wind-tunnel measurement, k-ε model, DES model, CFD.

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Authors: Ziraguen O. Williams, Shield B. Lin, Fouad N. Matari, Leslie J. Quiocho

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Simulation for seated row exercise was a continued task to assist NASA in analyzing a one-dimensional vibration isolation and stabilization system for astronaut’s exercise platform. Feedback delay and signal noise were added to the simulation model. Simulation runs for this study were conducted in two software simulation tools, Trick and MBDyn, software simulation environments developed at the NASA Johnson Space Center. The exciter force in the simulation was calculated from motion capture of an exerciser during a seated aerobic row exercise. The simulation runs include passive control, active control using a Proportional, Integral, Derivative (PID) controller, and active control using a Piecewise Linear Integral Derivative (PWLID) controller. Output parameters include displacements of the exercise platform, the exerciser, and the counterweight; transmitted force to the wall of spacecraft; and actuator force to the platform. The simulation results showed excellent force reduction in the active controlled system compared to the passive controlled system, which showed less force reduction.

Keywords: Simulation, counterweight, exercise, vibration.

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Authors: Zohir Irki, Michel Devy

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In this paper, we will present an architecture for the implementation of a real time stereoscopic images correction's approach. This architecture is parallel and makes use of several memory blocs in which are memorized pre calculated data relating to the cameras used for the acquisition of images. The use of reduced images proves to be essential in the proposed approach; the suggested architecture must so be able to carry out the real time reduction of original images.

Keywords: Image reduction, Real-time correction, Parallel architecture, Parallel treatment.

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Authors: L. Al Ahmad, C. Latrille, D. Hainos, D. Blanc, M. Clausse

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A two-dimensional finite volume axisymmetric model is developed to predict the simultaneous heat and mass transfers during the drying of industrial sludge. The simulations were run using COMSOL-Multiphysics 3.5a. The input parameters of the numerical model were acquired from a preliminary experimental work. Results permit to establish correlations describing the evolution of the various parameters as a function of the drying temperature and the sludge water content. The selection and coupling of the equation are validated based on the drying kinetics acquired experimentally at a temperature range of 45-65 °C and absolute pressure range of 200-1000 mbar. The model, incorporating the heat and mass transfer mechanisms at different operating conditions, shows simulated values of temperature and water content. Simulated results are found concordant with the experimental values, only at the first and last drying stages where sludge shrinkage is insignificant. Simulated and experimental results show that sludge drying is favored at high temperatures and low pressure. As experimentally observed, the drying time is reduced by 68% for drying at 65 °C compared to 45 °C under 1 atm. At 65 °C, a 200-mbar absolute pressure vacuum leads to an additional reduction in drying time estimated by 61%. However, the drying rate is underestimated in the intermediate stage. This rate underestimation could be improved in the model by considering the shrinkage phenomena that occurs during sludge drying.

Keywords: Industrial sludge drying, heat transfer, mass transfer, mathematical modelling.

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Authors: Y. N. Phang, E. F. Loh

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The zero truncated model is usually used in modeling count data without zero. It is the opposite of zero inflated model. Zero truncated Poisson and zero truncated negative binomial models are discussed and used by some researchers in analyzing the abundance of rare species and hospital stay. Zero truncated models are used as the base in developing hurdle models. In this study, we developed a new model, the zero truncated strict arcsine model, which can be used as an alternative model in modeling count data without zero and with extra variation. Two simulated and one real life data sets are used and fitted into this developed model. The results show that the model provides a good fit to the data. Maximum likelihood estimation method is used in estimating the parameters.

Keywords: Hurdle models, maximum likelihood estimation method, positive count data.

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Authors: Nihan Cinar

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Location selection is one of the most important decision making process which requires to consider several criteria based on the mission and the strategy. This study-s object is to provide a decision support model in order to help the bank selecting the most appropriate location for a bank-s branch considering a case study in Turkey. The object of the bank is to select the most appropriate city for opening a branch among six alternatives in the South-Eastern of Turkey. The model in this study was consisted of five main criteria which are Demographic, Socio-Economic, Sectoral Employment, Banking and Trade Potential and twenty one subcriteria which represent the bank-s mission and strategy. Because of the multi-criteria structure of the problem and the fuzziness in the comparisons of the criteria, fuzzy AHP is used and for the ranking of the alternatives, TOPSIS method is used.

Keywords: MCDM, bank branch location, fuzzy AHP, TOPSIS.

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Authors: M. Kovac

Abstract:

This article describes design of the 8-bit asynchronous microcontroller simulation model in VHDL. The model is created in ISE Foundation design tool and simulated in Modelsim tool. This model is a simple application example of asynchronous systems designed in synchronous design tools. The design process of creating asynchronous system with 4-phase bundled-data protocol and with matching delays is described in the article. The model is described in gate-level abstraction. The simulation waveform of the functional construction is the result of this article. Described construction covers only the simulation model. The next step would be creating synthesizable model to FPGA.

Keywords: Asynchronous, Microcontroller, VHDL, FPGA.

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Authors: GuoQiang Peng, Yi Sun

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In this paper, based on the work in [1], we further give a general model for acquiring knowledge, which first focuses on the research of how and when things involved in problems are made then describes the goals, the energy and the time to give an optimum model to decide how many related things are supposed to be involved in. Finally, we acquire knowledge from this model in which there are the attributes, actions and connections of the things involved at the time when they are born and the time in their life. This model not only improves AI theories, but also surely brings the effectiveness and accuracy for AI system because systems are given more knowledge when reasoning or computing is used to bring about results.

Keywords: Time, knowledge, model.

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

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In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Norfadzila, S.W.A., Balakrishnan, V., A. Abrizah

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The purpose of this paper is to propose an integrated consumer health informatics utilization framework that can be used to gauge the online health information needs and usage patterns among Malaysian women. The proposed framework was developed based on four different theories/models: Use and Gratification Theory, Technology Acceptance 3 Model, Health Belief Model, and Multi-level Model of Information Seeking. The relevant constructs and research hypotheses are also presented in this paper. The framework will be tested in order for it to be used successfully to identify Malaysian women-s preferences of online health information resources and health information seeking activities.

Keywords: Consumer Health Informatics, Consumer Preferences, Information Needs and Usage Patterns, Online Health Information, Women Studies

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Authors: Abdulsalam A. Al-Sudairi

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Object-oriented simulation is considered one of the most sophisticated techniques that has been widely used in planning, designing, executing and maintaining construction projects. This technique enables the modeler to focus on objects which is extremely important for thorough understanding of a system. Thus, identifying an object is an essential point of building a successful simulation model. In a maintenance process an object is a maintenance work order (MWO). This study demonstrates a maintenance simulation model for the building maintenance division of Saudi Consolidated Electric Company (SCECO) in Dammam, Saudi Arabia. The model focused on both types of maintenance processes namely: (1) preventive maintenance (PM) and (2) corrective maintenance (CM). It is apparent from the findings that object-oriented simulation is a good diagnostic and experimental tool. This is because problems, limitations, bottlenecks and so forth are easily identified. These features are very difficult to obtain when using other tools.

Keywords: Object oriented, simulation, maintenance, process, work orders

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Authors: Toshihiko Matsuka

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One problem in evaluating recent computational models of human category learning is that there is no standardized method for systematically comparing the models' assumptions or hypotheses. In the present study, a flexible general model (called GECLE) is introduced that can be used as a framework to systematically manipulate and compare the effects and descriptive validities of a limited number of assumptions at a time. Two example simulation studies are presented to show how the GECLE framework can be useful in the field of human high-order cognition research.

Keywords: artificial intelligence, category learning, cognitive modeling, radial basis functions.

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Authors: Kahil Amar, Meziani Faroudja, Khelil Nacim

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The principal objective of this study is the evaluation of the seismic performance of reinforced concrete frame structures, taking into account of the behavior laws, reflecting the real behavior of materials, using CASTEM2000 software. A finite element model used is based in modified Takeda model with Timoshenko elements for columns and beams. This model is validated on a Vecchio experimental reinforced concrete (RC) frame model. Then, a study focused on the behavior of a RC frame with three-level and three-story in order to visualize the positioning the plastic hinge (plastic rotation), determined from the curvature distribution along the elements. The results obtained show that the beams of the 1^st and 2^nd level developed a very large plastic rotations, or these rotations exceed the values corresponding to CP (Collapse prevention with cp q_CP = 0.02 rad), against those developed at the 3^rd level, are between IO and LS (Immediate occupancy and life Safety with q_IO = 0.005 rad and rad q_LS = 0.01 respectively), so the beams of first and second levels submit a very significant damage.

Keywords: Seismic performance, performance level, pushover analysis, plastic rotation, plastic hinge.

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Authors: Omar A Shaneb, Adell S. Amer

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Reduction of CO2 emissions has become a priority for several countries due to increasing concerns about global warming and climate change, especially in the developed countries. Residential sector is considered one of the most important sectors for considerable reduction of CO2 emissions since it represents a significant amount of the total consumed energy in those countries. A significant CO2 reduction cannot be achieved unless some initiatives have been adopted in the policy of these countries. Introducing micro combined heat and power (!CHP) systems into residential energy systems is one of these initiatives, since such a technology offers several advantages. Moreover, !CHP technology has the opportunity to be operated not only by natural gas but it could also be operated by renewable fuels. However, this technology can be operated by different operation strategies. Each strategy has some advantages and disadvantages. This paper provides a review of different operation strategies of such a technology used for residential energy systems, especially for single dwellings. The review summarizes key points that outline the trend of previous research carried out in this field.

Keywords: Energy management, !CHP systems, residential energy systems, sustainable houses, operation strategy.

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Authors: HoYoung Son, Ki Young Kim, Woo Young Jung

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This study investigated the change of weir structure performances when durability of concrete, which is the main material of weir structure, decreased due to their aging by mean of seismic fragility analysis. In the analysis, it was assumed that the elastic modulus of concrete was reduced by 10% in order to account for their aged deterioration. Additionally, the analysis of seismic fragility was based on Monte Carlo Simulation method combined with a 2D nonlinear finite element in ABAQUS platform with the consideration of deterioration of concrete. Finally, the comparison of seismic fragility of model pre- and post-deterioration was made to study the performance of weir. Results show that the probability of failure in moderate damage for deteriorated model was found to be larger than pre-deterioration model when peak ground acceleration (PGA) passed 0.4 g.

Keywords: Weir, FEM, concrete, fragility, aging.

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Authors: Jawad Saleem, Abdul Majid, Kent Bertilsson, Torbjörn Carlberg, Nazar Ul Islam

Abstract:

Resistance spot welding process comprises of electric, thermal and mechanical phenomenon, which makes this process complex and highly non-linear and thus, it becomes difficult to model it. In order to obtain good weld nugget during spot welding, hit and trial welds are usually done which is very costly. Therefore the numerical simulation research has been conducted to understand the whole process. In this paper three different cases were analyzed by varying the tip contact area and it was observed that, with the variation of tip contact area the nugget formation at the faying surface is affected. The tip contact area of the welding electrode becomes large with long welding cycles. Therefore in order to maintain consistency of nugget formation during the welding process, the current compensation in control feedback is required. If the contact area of the welding electrode tip is reduced, a large amount of current flows through the faying surface, as a result of which sputtering occurs.

Keywords: Resistance spot welding, Finite element modeling, Nugget formation, Welding electrode, Numerical method simulation,

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Authors: Ronal Muresano, Andrea Pagano

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Nowadays, the mathematical/statistical applications are developed with more complexity and accuracy. However, these precisions and complexities have brought as result that applications need more computational power in order to be executed faster. In this sense, the multicore environments are playing an important role to improve and to optimize the execution time of these applications. These environments allow us the inclusion of more parallelism inside the node. However, to take advantage of this parallelism is not an easy task, because we have to deal with some problems such as: cores communications, data locality, memory sizes (cache and RAM), synchronizations, data dependencies on the model, etc. These issues are becoming more important when we wish to improve the application’s performance and scalability. Hence, this paper describes an optimization method developed for Systemic Model of Banking Originated Losses (SYMBOL) tool developed by the European Commission, which is based on analyzing the application's weakness in order to exploit the advantages of the multicore. All these improvements are done in an automatic and transparent manner with the aim of improving the performance metrics of our tool. Finally, experimental evaluations show the effectiveness of our new optimized version, in which we have achieved a considerable improvement on the execution time. The time has been reduced around 96% for the best case tested, between the original serial version and the automatic parallel version.

Keywords: Algorithm optimization, Bank Failures, OpenMP, Parallel Techniques, Statistical tool.

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Authors: Fares Laouacheria, Said Kechida, Moncef Chabi

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The objective of the study was based on the hydrological routing modelling for the continuous monitoring of the hydrological situation in the Moudjar river catchment, especially during floods with Hydrologic Engineering Center–Hydrologic Modelling Systems (HEC-HMS). The HEC-GeoHMS was used to transform data from geographic information system (GIS) to HEC-HMS for delineating and modelling the catchment river in order to estimate the runoff volume, which is used as inputs to the hydrological routing model. Two hydrological routing models were used, namely Muskingum and Muskingum routing models, for conducting this study. In this study, a comparison between the parameters of the Muskingum and Muskingum-Cunge routing models in HEC-HMS was used for modelling flood routing in the Moudjar river catchment and determining the relationship between these parameters and the physical characteristics of the river. The results indicate that the effects of input parameters such as the weighting factor "X" and travel time "K" on the output results are more significant, where the Muskingum routing model was more sensitive to input parameters than the Muskingum-Cunge routing model. This study can contribute to understand and improve the knowledge of the mechanisms of river floods, especially in ungauged river catchments.

Keywords: HEC-HMS, hydrological modelling, Muskingum routing model, Muskingum-Cunge routing model.

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Authors: Karunakar A K, Manohara Pai M M

Abstract:

In 3D-wavelet video coding framework temporal filtering is done along the trajectory of motion using Motion Compensated Temporal Filtering (MCTF). Hence computationally efficient motion estimation technique is the need of MCTF. In this paper a predictive technique is proposed in order to reduce the computational complexity of the MCTF framework, by exploiting the high correlation among the frames in a Group Of Picture (GOP). The proposed technique applies coarse and fine searches of any fast block based motion estimation, only to the first pair of frames in a GOP. The generated motion vectors are supplied to the next consecutive frames, even to subsequent temporal levels and only fine search is carried out around those predicted motion vectors. Hence coarse search is skipped for all the motion estimation in a GOP except for the first pair of frames. The technique has been tested for different fast block based motion estimation algorithms over different standard test sequences using MC-EZBC, a state-of-the-art scalable video coder. The simulation result reveals substantial reduction (i.e. 20.75% to 38.24%) in the number of search points during motion estimation, without compromising the quality of the reconstructed video compared to non-predictive techniques. Since the motion vectors of all the pair of frames in a GOP except the first pair will have value ±1 around the motion vectors of the previous pair of frames, the number of bits required for motion vectors is also reduced by 50%.

Keywords: Motion Compensated Temporal Filtering, predictivemotion estimation, lifted wavelet transform, motion vector

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Authors: Erika Ruíz, Luis Amaya, Diego Carreño

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The main objective of this study is to design a mathematical model for the logistics of mining collection centers in the northern region of the department of Boyacá (Colombia), determining the structure that facilitates the flow of products along the supply chain. In order to achieve this, it is necessary to define a suitable design of the distribution network, taking into account the products, customer’s characteristics and the availability of information. Likewise, some other aspects must be defined, such as number and capacity of collection centers to establish, routes that must be taken to deliver products to the customers, among others. This research will use one of the operation research problems, which is used in the design of distribution networks known as Location Routing Problem (LRP).

Keywords: Location routing problem, logistic, mining collection, model.

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Authors: Ahmed Abbas Helmy, M. R. M. Rizk, Mohamed El-Sayed

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A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

Keywords: Adaptive control, model predictive control, dynamic matrix control, online model identification

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Authors: Guo Xiuhua, Sun Tao, Wu Haifeng, He Wen, Liang Zhigang, Zhang Mengxia, Guo Aimin, Wang Wei

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Purpose: To explore the use of Curvelet transform to extract texture features of pulmonary nodules in CT image and support vector machine to establish prediction model of small solitary pulmonary nodules in order to promote the ratio of detection and diagnosis of early-stage lung cancer. Methods: 2461 benign or malignant small solitary pulmonary nodules in CT image from 129 patients were collected. Fourteen Curvelet transform textural features were as parameters to establish support vector machine prediction model. Results: Compared with other methods, using 252 texture features as parameters to establish prediction model is more proper. And the classification consistency, sensitivity and specificity for the model are 81.5%, 93.8% and 38.0% respectively. Conclusion: Based on texture features extracted from Curvelet transform, support vector machine prediction model is sensitive to lung cancer, which can promote the rate of diagnosis for early-stage lung cancer to some extent.

Keywords: CT image, Curvelet transform, Small pulmonary nodules, Support vector machines, Texture extraction.

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Authors: Hamed Sabahno

Abstract:

In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.

Keywords: Deteriorating items, Dynamic programming, Finitereplenishment rate, Inventory control, Operation Research.

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