Search results for: Greedy alignment procedure

Authors: Alexander Goncharenko, Andrey Denisov, Sergey Alyamkin, Evgeny Terentev

Abstract:

The neural network quantization is highly desired procedure to perform before running neural networks on mobile devices. Quantization without fine-tuning leads to accuracy drop of the model, whereas commonly used training with quantization is done on the full set of the labeled data and therefore is both time- and resource-consuming. Real life applications require simplification and acceleration of quantization procedure that will maintain accuracy of full-precision neural network, especially for modern mobile neural network architectures like Mobilenet-v1, MobileNet-v2 and MNAS. Here we present a method to significantly optimize training with quantization procedure by introducing the trained scale factors for discretization thresholds that are separate for each filter. Using the proposed technique, we quantize the modern mobile architectures of neural networks with the set of train data of only ∼ 10% of the total ImageNet 2012 sample. Such reduction of train dataset size and small number of trainable parameters allow to fine-tune the network for several hours while maintaining the high accuracy of quantized model (accuracy drop was less than 0.5%). Ready-for-use models and code are available in the GitHub repository.

Keywords: Distillation, machine learning, neural networks, quantization.

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Authors: Othman Maklouf, Ahmed Adwaib

Abstract:

This paper introduces a comparative study between the main GPS\INS coupling schemes, this will include the loosely coupled and tightly coupled configurations, several types of situations and operational conditions, in which the data fusion process is done using Kalman filtering. This will include the importance of sensors calibration as well as the alignment of the strap down inertial navigation system. The limitations of the inertial navigation systems are investigated.

Keywords: GPS, INS, Kalman Filter.

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Authors: J. Cheeneebash, S. Jugee

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In this paper, the Tabu search algorithm is used to solve a transportation problem which consists of determining the shortest routes with the appropriate vehicle capacity to facilitate the travel of the students attending the University of Mauritius. The aim of this work is to minimize the total cost of the distance travelled by the vehicles in serving all the customers. An initial solution is obtained by the TOUR algorithm which basically constructs a giant tour containing all the customers and partitions it in an optimal way so as to produce a set of feasible routes. The Tabu search algorithm then makes use of a search procedure, a swapping procedure and the intensification and diversification mechanism to find the best set of feasible routes.

Keywords: Tabu Search, Vehicle Routing, Transport.

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Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

Abstract:

Influence and influence diffusion have been studied extensively in social networks. However, most existing literature on this task are limited on static networks, ignoring the fact that the interactions between users change over time. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time is studied. The DM algorithm is an extension of Matrix Influence (MATI) algorithm and solves the Influence Maximization (IM) problem in dynamic networks and is proposed under the Linear Threshold (LT) and Independent Cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: Influence maximization, dynamic social networks, diffusion, social influence.

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Authors: R. Geetha, G. Umarani Srikanth, S. Prabhu

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Wireless sensor networks are resource constrained networks, where energy is the major resource in such networks. Therefore, energy conservation is major aspect in the deployment of Wireless Sensor Network. This work makes use of an extended Greedy Perimeter Stateless Routing (eGPSR) protocol that mainly focuses on energy efficient data transmission. This data transmission is based on the fact that the message that is sent to a distant node consumes more energy than the message that is sent to a short range transmission. Every cluster contains a head set that consists of many virtual cluster heads. Routing is decided by head set members. The energy level of the received signal is the major constraint to choose head set from its members. The experimental result shows that the use of eGPSR in routing has improved throughput with comparatively less delay.

Keywords: eGPSR, energy efficiency, routing, wireless sensor networks, WSN.

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Authors: S. A. Faizi, S. Yoshitomi

Abstract:

The optimal design procedure of buckling restrained braces (BRBs) in reinforced concrete (RC) building structures can provide the distribution of horizontal stiffness of BRBs at each story, which minimizes story drift response of the structure under the constraint of specified total stiffness of BRBs. In this paper, a simple rule is proposed to convert continuous horizontal stiffness of BRBs into sectional sizes of BRB which are available from standardized section list assuming realistic structural design stage.

Keywords: Buckling restrained brace, building engineering, optimal damper placement, structural engineering.

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Authors: Qasim Kriri, Harsh B. Desai

Abstract:

Water supply and sanitation in Saudi Arabia is portrayed by difficulties and accomplishments. One of the fundamental difficulties is water shortage. With a specific end goal to beat water shortage, significant ventures have been attempted in sea water desalination, water circulation, sewerage, and wastewater treatment. The motivation behind Statistical Process Control (SPC) is to decide whether the execution of a procedure is keeping up an acceptable quality level [AQL]. SPC is an analytical decision-making method. A fundamental apparatus in the SPC is the Control Charts, which follow the inconstancy in the estimations of the item quality attributes. By utilizing the suitable outline, administration can decide whether changes should be made with a specific end goal to keep the procedure in charge. The two most important quality factors in the distilled water which were taken into consideration were pH (Potential of Hydrogen) and TDS (Total Dissolved Solids). There were three stages at which the quality checks were done. The stages were as follows: (1) Water at the source, (2) water after chemical treatment & (3) water which is sent for packing. The upper specification limit, central limit and lower specification limit are taken as per Saudi water standards. The procedure capacity to accomplish the particulars set for the quality attributes of Berain water Factory chose to be focused by the proposed SPC system.

Keywords: Acceptable quality level, statistical quality control, control charts, process charts.

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Authors: Carlos L. Antunes, Tony R. Almeida, Nélia Raposeiro, Belarmino Gonçalves, Paulo Almeida, André Antunes

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In the last two decades radiofrequency ablation (RFA) has been considered a promising medical procedure for the treatment of primary and secondary malignancies. However, the needle-based electrodes so far developed for this kind of treatment are not suitable for the thermal ablation of tumors located in hollow organs like esophagus, colon or bile duct. In this work a tubular electrode solution is presented. Numerical and experimental analyses were performed to characterize the volume of the lesion induced. Results show that this kind of electrode is a feasible solution and numerical simulation might provide a tool for planning RFA procedure with some accuracy.

Keywords: 3D modeling, cancer, medical therapy, radiofrequency ablation.

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Authors: P I Jagad, B P Puranik, A W Date

Abstract:

Flow through micro and mini channels requires relatively high driving pressure due to the large fluid pressure drop through these channels. Consequently the forces acting on the walls of the channel due to the fluid pressure are also large. Due to these forces there are displacement fields set up in the solid substrate containing the channels. If the movement of the substrate is constrained at some points, then stress fields are established in the substrate. On the other hand, if the deformation of the channel shape is sufficiently large then its effect on the fluid flow is important to be calculated. Such coupled fluid-solid systems form a class of problems known as fluidstructure interactions. In the present work a co-located finite volume discretization procedure on unstructured meshes is described for solving fluid-structure interaction type of problems. A linear elastic solid is assumed for which the effect of the channel deformation on the flow is neglected. Thus the governing equations for the fluid and the solid are decoupled and are solved separately. The procedure is validated by solving two benchmark problems, one from fluid mechanics and another from solid mechanics. A fluid-structure interaction problem of flow through a U-shaped channel embedded in a plate is solved.

Keywords: Finite volume method, flow induced stresses, fluidstructureinteraction, unstructured meshes.

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Authors: Jingming Wu, Ruikang Hu, Junqi Yue, Zhaoguang Yang, Lifeng Zhang

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Fecal sterol has been proposed as a chemical indicator of human fecal pollution even when fecal coliform populations have diminished due to water chlorination or toxic effects of industrial effluents. This paper describes an improved derivatization procedure for simultaneous determination of four fecal sterols including coprostanol, epicholestanol, cholesterol and cholestanol using gas chromatography-mass spectrometry (GC-MS), via optimization study on silylation procedures using N-O-bis (trimethylsilyl)-trifluoroacetamide (BSTFA), and N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA), which lead to the formation of trimethylsilyl (TMS) and tert-butyldimethylsilyl (TBS) derivatives, respectively. Two derivatization processes of injection-port derivatization and water bath derivatization (60 oC, 1h) were inspected and compared. Furthermore, the methylation procedure at 25 oC for 2h with trimethylsilydiazomethane (TMSD) for fecal sterols analysis was also studied. It was found that most of TMS derivatives demonstrated the highest sensitivities, followed by methylated derivatives. For BSTFA or MTBSTFA derivatization processes, the simple injection-port derivatization process could achieve the same efficiency as that in the tedious water bath derivatization procedure.

Keywords: Fecal Sterols, Methylation, Silylation, BSTFA, MTBSTFA, TMSD, GC-MS.

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Authors: Jingming Wu, Ruikang Hu, Junqi Yue, Zhaoguang Yang, Lifeng Zhang

Abstract:

Fecal sterol has been proposed as a chemical indicator of human fecal pollution even when fecal coliform populations have diminished due to water chlorination or toxic effects of industrial effluents. This paper describes an improved derivatization procedure for simultaneous determination of four fecal sterols including coprostanol, epicholestanol, cholesterol and cholestanol using gas chromatography-mass spectrometry (GC-MS), via optimization study on silylation procedures using N-O-bis (trimethylsilyl)-trifluoroacetamide (BSTFA), and N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA), which lead to the formation of trimethylsilyl (TMS) and tert-butyldimethylsilyl (TBS) derivatives, respectively. Two derivatization processes of injection-port derivatization and water bath derivatization (60 oC, 1h) were inspected and compared. Furthermore, the methylation procedure at 25 oC for 2h with trimethylsilydiazomethane (TMSD) for fecal sterols analysis was also studied. It was found that most of TMS derivatives demonstrated the highest sensitivities, followed by methylated derivatives. For BSTFA or MTBSTFA derivatization processes, the simple injection-port derivatization process could achieve the same efficiency as that in the tedious water bath derivatization procedure.

Keywords: Fecal Sterols, Methylation, Silylation, BSTFA, MTBSTFA, TMSD, GC-MS.

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Authors: Pilar Rey-del-Castillo, Jesús Cardeñosa

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There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson-s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Keywords: Classifier, imputation techniques, fuzzy systems, fuzzy min-max neural networks.

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Authors: L. Korpinen, P. Taskinen, P. Rautio

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This study aimed to describe procedures that we developed to use in the quantitative, bone-specific SPECT/CT at our hospital. Our procedures included the following questions for choosing imaging protocols, which were based on a clinical doctor's referral: (1) Is she/he a cancer patient or not? (2) Are there any indications of inflammatory rheumatoid arthritis? We performed about 1,106 skeletal scintigraphies over two years. About 394 patients were studied with quantitative bone-specific single-photon emission computed tomography/computerized tomography (SPECT/CT) (i.e., about 36% of all bone scintigraphies). Approximately 64% of the patients were studied using the conventional Anterior-Posterior/Posterior-Anterior imaging. Our procedure has improved efficiency and decreased cycle times.

Keywords: Skeletal scintigraphy, SPECT/CT, imaging.

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Authors: M. Kotobuki, M. Koishi

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Li1.5Al0.5Ti1.5 (PO4)3(LATP) has received much attention as a solid electrolyte for lithium batteries. In this study, the LATP solid electrolyte is prepared by the co-precipitation method using Li3PO4 as a Li source. The LATP is successfully prepared and the Li ion conductivities of bulk (inner crystal) and total (inner crystal and grain boundary) are 1.1 × 10-3 and 1.1 × 10-4 S cm-1, respectively. These values are comparable to the reported values, in which Li2C2O4 is used as the Li source. It is conclude that the LATP solid electrolyte can be prepared by the co-precipitation method using Li3PO4 as the Li source and this procedure has an advantage in mass production over previous procedure using Li2C2O4 because Li3PO4 is lower price reagent compared with Li2C2O4.

Keywords: Co-precipitation method, lithium battery, NASICON-type electrolyte, solid electrolyte.

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Authors: Frantisek Bozek, Alena Bumbova, Eduard Bakos

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Paper is dealing with vulnerability concerning elements of hydrological structures and elements of technological equipments which are acceptable for groundwater resources. The vulnerability assessment stems from the application of the register of hazards and a potential threat to individual water source elements within each type of hazard. The proposed procedure is pattern for assessing the risks of disturbance, damage, or destruction of water source by the identified natural or technological hazards and consequently for classification of these risks in relation to emergency water supply. Using of this procedure was verified on selected groundwater resource in particular region, which seems to be as potentially useful for crisis planning system.

Keywords: Hazard, Hydrogeological Structure, Elements, Index, Sensitivity, Water Source, Vulnerability

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Authors: Anwar Jarndal

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In this paper, a genetic-neural-network (GNN) based large-signal model for GaN HEMTs is presented along with its parameters extraction procedure. The model is easy to construct and implement in CAD software and requires only DC and S-parameter measurements. An improved decomposition technique is used to model self-heating effect. Two GNN models are constructed to simulate isothermal drain current and power dissipation, respectively. The two model are then composed to simulate the drain current. The modeling procedure was applied to a packaged GaN-on-Si HEMT and the developed model is validated by comparing its large-signal simulation with measured data. A very good agreement between the simulation and measurement is obtained.

Keywords: GaN HEMT, computer-aided design & modeling, neural networks, genetic optimization.

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Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte

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This paper proposes a bioprocess optimization procedure based on Relevance Vector Regression models and evolutionary programming technique. Relevance Vector Regression scheme allows developing a compact and stable data-based process model avoiding time-consuming modeling expenses. The model building and process optimization procedure could be done in a half-automated way and repeated after every new cultivation run. The proposed technique was tested in a simulated mammalian cell cultivation process. The obtained results are promising and could be attractive for optimization of industrial bioprocesses.

Keywords: Bioprocess optimization, Evolutionary programming, Relevance Vector Regression.

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Authors: A. Farshidianfar, P. Oliazadeh, M. H. Farshidianfar

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In order to study the free vibration of simply supported circular cylindrical shells; an analytical procedure is developed and discussed in detail. To identify its’ validity, the exact technique was applied to four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter, and 4) Donnell. The exact procedure was compared favorably with experimental results and those obtained using the numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The effects of this approximate method were also investigated on the natural frequencies by comparing results with those of the exact analysis.

Keywords: Circular Cylindrical Shell, Free Vibration, Natural Frequency.

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Authors: B. O. Olawale, C. R. Chatwin, R. C. D. Young, P. M. Birch, F. O. Faithpraise, A. O. Olukiran

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In this paper, we present a four-step ortho-rectification procedure for real-time geo-referencing of video data from a low-cost UAV equipped with a multi-sensor system. The basic procedures for the real-time ortho-rectification are: (1) decompilation of the video stream into individual frames; (2) establishing the interior camera orientation parameters; (3) determining the relative orientation parameters for each video frame with respect to each other; (4) finding the absolute orientation parameters, using a self-calibration bundle and adjustment with the aid of a mathematical model. Each ortho-rectified video frame is then mosaicked together to produce a mosaic image of the test area, which is then merged with a well referenced existing digital map for the purpose of geo-referencing and aerial surveillance. A test field located in Abuja, Nigeria was used to evaluate our method. Video and telemetry data were collected for about fifteen minutes, and they were processed using the four-step ortho-rectification procedure. The results demonstrated that the geometric measurement of the control field from ortho-images is more accurate when compared with those from original perspective images when used to pin point the exact location of targets on the video imagery acquired by the UAV. The 2-D planimetric accuracy when compared with the 6 control points measured by a GPS receiver is between 3 to 5 metres.

Keywords: Geo-referencing, ortho-rectification, video frame, self-calibration, UAV, target tracking.

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Authors: Dimitrios Koukopoulos

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In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, ¤ü)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates ¤ü > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.

Keywords: Network stability, quality of service, adversarial queueing theory, greedy scheduling protocols.

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Authors: Dimitrios Koukopoulos

Abstract:

In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, p)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates p > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.

Keywords: Parallel computing, network stability, adversarial queuing theory, greedy scheduling protocols.

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

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This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: Melting furnace, inverse heat transfer, enthalpy method, Levenberg–Marquardt Method.

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Authors: Firouz Parvizian Ganje, Emad Hezbkhah, Behbood Maashkar

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Climate change could lead to changes in cultural environments and landscapes as we know them.Climate change presents an immediate and significant threat to our natural and built environments and to the ways of life which co-exist with these environments. In most traditional buildings, the harmony of texture with nature and environment has been ever considered; so houses and cities have been mixed with their natural environment so astonishingly and the selection and usage of materials have been in such a way that they have provided the utmost conformity with the environment, as the result the created areas have a unique beauty and attraction.The extent to which climate change contributes to destruction procedure on Iran-s historic buildings.is a subject of current discussion. Cities, towns and built-up areas also have their own characteristics that might make them particularly vulnerable to climate change.

Keywords: Climate Change, historic buildings, Iran

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Authors: Jianjun Yuan, Changjun Jiang

Abstract:

Pairwise testing, which requires that every combination of valid values of each pair of system factors be covered by at lease one test case, plays an important role in software testing since many faults are caused by unexpected 2-way interactions among system factors. Although meta-heuristic strategies like simulated annealing can generally discover smaller pairwise test suite, they may cost more time to perform search, compared with greedy algorithms. We propose a new method, improved Extremal Optimization (EO) based on the Bak-Sneppen (BS) model of biological evolution, for constructing pairwise test suites and define fitness function according to the requirement of improved EO. Experimental results show that improved EO gives similar size of resulting pairwise test suite and yields an 85% reduction in solution time over SA.

Keywords: Covering Arrays, Extremal Optimization, Simulated Annealing, Software Testing.

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Authors: Siyuan Jing, Kun She

Abstract:

Neighborhood Rough Sets (NRS) has been proven to be an efficient tool for heterogeneous attribute reduction. However, most of researches are focused on dealing with complete and noiseless data. Factually, most of the information systems are noisy, namely, filled with incomplete data and inconsistent data. In this paper, we introduce a generalized neighborhood rough sets model, called VPTNRS, to deal with the problem of heterogeneous attribute reduction in noisy system. We generalize classical NRS model with tolerance neighborhood relation and the probabilistic theory. Furthermore, we use the neighborhood dependency to evaluate the significance of a subset of heterogeneous attributes and construct a forward greedy algorithm for attribute reduction based on it. Experimental results show that the model is efficient to deal with noisy data.

Keywords: attribute reduction, incomplete data, inconsistent data, tolerance neighborhood relation, rough sets

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Authors: S. Vasupongayya, W. Noodam, P. Kongyong

Abstract:

This paper presents the result of three senior capstone projects at the Department of Computer Engineering, Prince of Songkla University, Thailand. These projects focus on developing an examination management system for the Faculty of Engineering in order to manage the examination both the examination room assignments and the examination proctor assignments in each room. The current version of the software is a web-based application. The developed software allows the examination proctors to select their scheduled time online while each subject is assigned to each available examination room according to its type and the room capacity. The developed system is evaluated using real data by prospective users of the system. Several suggestions for further improvements are given by the testers. Even though the features of the developed software are not superior, the developing process can be a case study for a projectbased teaching style. Furthermore, the process of developing this software can show several issues in developing an educational support application.

Keywords: Scheduling, Web-based, Greedy Algorithm, Engineering Education.

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Authors: Christian Bräuer-Burchardt, Peter Kühmstedt, Gunther Notni

Abstract:

A new hybrid method to realise high-precision distortion determination for optical ultra-precision 3D measurement systems based on stereo cameras using active light projection is introduced. It consists of two phases: the basic distortion determination and the refinement. The refinement phase of the procedure uses a plane surface and projected fringe patterns as calibration tools to determine simultaneously the distortion of both cameras within an iterative procedure. The new technique may be performed in the state of the device “ready for measurement" which avoids errors by a later adjustment. A considerable reduction of distortion errors is achieved and leads to considerable improvements of the accuracy of 3D measurements, especially in the precise measurement of smooth surfaces.

Keywords: 3D Surface Measurement, Fringe Projection, Lens Distortion, Stereo.

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Authors: Qing Lyu, Hang Zhu

Abstract:

Various flows in the network require to go through different types of middlebox. The improper placement of network middlebox and path assignment for flows could greatly increase the network latency and also decrease the performance of network. Minimizing the total end to end latency of all the ows requires to assign path for the incoming flows. In this paper, the flow path assignment problem in regard to the placement of various kinds of middlebox is studied. The flow path assignment problem is formulated to a linear programming problem, which is very time consuming. On the other hand, a naive greedy algorithm is studied. Which is very fast but causes much more latency than the linear programming algorithm. At last, the paper presents a heuristic algorithm named FPA, which takes bottleneck link information and estimated bandwidth occupancy into consideration, and achieves near optimal latency in much less time. Evaluation results validate the effectiveness of the proposed algorithm.

Keywords: Latency, Fast path assignment, Bottleneck link.

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Authors: Mhand Hifi, Hedi Mhalla

Abstract:

In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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