Search results for: Piecewise DerivativeDynamic Time Warping.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6534

Search results for: Piecewise DerivativeDynamic Time Warping.

6474 Calibration of Time-Skew Error in a M-Channel Time-Interleaved Analog-to-Digital Converter

Authors: Yu-Sheng Lee, Qi An

Abstract:

Offset mismatch, gain mismatch, and time-skew error between time-interleaved channels limit the performance of time-interleaved analog-to-digital converters (TIADC). This paper focused on the time-skew error. A new technique for calibrating time-skew error in M-channels TIADC is described, and simulation results are also presented.

Keywords: Calibration, time-skew error, time-interleavedanalog-to-digital converters.

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6473 Identification of a PWA Model of a Batch Reactor for Model Predictive Control

Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic

Abstract:

The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.

Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.

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6472 Improving Image Segmentation Performance via Edge Preserving Regularization

Authors: Ying-jie Zhang, Li-ling Ge

Abstract:

This paper presents an improved image segmentation model with edge preserving regularization based on the piecewise-smooth Mumford-Shah functional. A level set formulation is considered for the Mumford-Shah functional minimization in segmentation, and the corresponding partial difference equations are solved by the backward Euler discretization. Aiming at encouraging edge preserving regularization, a new edge indicator function is introduced at level set frame. In which all the grid points which is used to locate the level set curve are considered to avoid blurring the edges and a nonlinear smooth constraint function as regularization term is applied to smooth the image in the isophote direction instead of the gradient direction. In implementation, some strategies such as a new scheme for extension of u+ and u- computation of the grid points and speedup of the convergence are studied to improve the efficacy of the algorithm. The resulting algorithm has been implemented and compared with the previous methods, and has been proved efficiently by several cases.

Keywords: Energy minimization, image segmentation, level sets, edge regularization.

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6471 The Feedback Control for Distributed Systems

Authors: Kamil Aida-zade, C. Ardil

Abstract:

We study the problem of synthesis of lumped sources control for the objects with distributed parameters on the basis of continuous observation of phase state at given points of object. In the proposed approach the phase state space (phase space) is beforehand somehow partitioned at observable points into given subsets (zones). The synthesizing control actions therewith are taken from the class of piecewise constant functions. The current values of control actions are determined by the subset of phase space that contains the aggregate of current states of object at the observable points (in these states control actions take constant values). In the paper such synthesized control actions are called zone control actions. A technique to obtain optimal values of zone control actions with the use of smooth optimization methods is given. With this aim, the formulas of objective functional gradient in the space of zone control actions are obtained.

Keywords: Feedback control, distributed systems, smooth optimization methods, lumped control synthesis.

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6470 Second-order Time Evolution Scheme for Time-dependent Neutron Transport Equation

Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

Abstract:

In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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6469 On the Differential Geometry of the Curves in Minkowski Space-Time II

Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut

Abstract:

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated.

Keywords: Frenet Apparatus, Time-like Curves, MinkowskiSpace-time.

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6468 Comparative Sulphate Resistance of Pozzolanic Cement Mortars

Authors: Mahmud Abba Tahir

Abstract:

This is report on experiment out to compare the sulphate resistance of sand mortar made with five different pozzolanic cement. The pozzolanic cement were prepared by blending powered burnt bricks from the Adamawa, Makurdi, Kano, Kaduna and Niger bricks factories with ordinary Portland cement in the ratio 1:4. Sand –pozzolanic cement mortars of mix ratio 1:6 and 1:3 with water-cement ratio of 0.65 and 0.40 respectively were used to prepare cubes and bars specimens. 150 mortar cubes of size 70mm x 70mm x 70mm and 35 mortar bars of 15mm x 15mm x 100mm dimensions were cast and cured for 28 days. The cured specimens then immersed in the solutions of K2SO4, (NH4)2SO4 and water for 28 days and then tested. The compressive strengths of cubes in water increased by 34% while those in the sulphate solutions decreased. Strength decreases of the cubes, cracking and warping of bars immersed in K2SO4 were less than those in (NH4)2SO4. Specimens made with Niger and Makurdi pulverized burnt bricks experienced less effect of the sulphates and can therefore be used as pozzolan in mortar and concrete to resist sulphate.

Keywords: Burnt bricks powder, comparative, pozzolanic cement, sulphates.

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6467 A Methodology for Reducing the BGP Convergence Time

Authors: Eatedal A. Alabdulkreem, Hamed S. Al-Raweshidy, Maysam F. Abbod

Abstract:

Border Gateway Protocol (BGP) is the standard routing protocol between various autonomous systems (AS) in the internet. In the event of failure, a considerable delay in the BGP convergence has been shown by empirical measurements. During the convergence time the BGP will repeatedly advertise new routes to some destination and withdraw old ones until it reach a stable state. It has been found that the KEEPALIVE message timer and the HOLD time are tow parameters affecting the convergence speed. This paper aims to find the optimum value for the KEEPALIVE timer and the HOLD time that maximally reduces the convergence time without increasing the traffic. The KEEPALIVE message timer optimal value founded by this paper is 30 second instead of 60 seconds, and the optimal value for the HOLD time is 90 seconds instead of 180 seconds.

Keywords: BGP, Convergence Time, HOLD time, Keep alive.

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6466 Linear Programming Application in Unit Commitment of Wind Farms with Considering Uncertainties

Authors: M. Esmaeeli Shahrakht, A. Kazemi

Abstract:

Due to uncertainty of wind velocity, wind power generators don’t have deterministic output power. Utilizing wind power generation and thermal power plants together create new concerns for operation engineers of power systems. In this paper, a model is presented to implement the uncertainty of load and generated wind power which can be utilized in power system operation planning. Stochastic behavior of parameters is simulated by generating scenarios that can be solved by deterministic method. A mixed-integer linear programming method is used for solving deterministic generation scheduling problem. The proposed approach is applied to a 12-unit test system including 10 thermal units and 2 wind farms. The results show affectivity of piecewise linear model in unit commitment problems. Also using linear programming causes a considerable reduction in calculation times and guarantees convergence to the global optimum. Neglecting the uncertainty of wind velocity causes higher cost assessment of generation scheduling.

Keywords: Load uncertainty, linear programming, scenario generation, unit commitment, wind farm.

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6465 Analysis and Research of Two-Level Scheduling Profile for Open Real-Time System

Authors: Yongxian Jin, Jingzhou Huang

Abstract:

In an open real-time system environment, the coexistence of different kinds of real-time and non real-time applications makes the system scheduling mechanism face new requirements and challenges. One two-level scheduling scheme of the open real-time systems is introduced, and points out that hard and soft real-time applications are scheduled non-distinctively as the same type real-time applications, the Quality of Service (QoS) cannot be guaranteed. It has two flaws: The first, it can not differentiate scheduling priorities of hard and soft real-time applications, that is to say, it neglects characteristic differences between hard real-time applications and soft ones, so it does not suit a more complex real-time environment. The second, the worst case execution time of soft real-time applications cannot be predicted exactly, so it is not worth while to cost much spending in order to assure all soft real-time applications not to miss their deadlines, and doing that may cause resource wasting. In order to solve this problem, a novel two-level real-time scheduling mechanism (including scheduling profile and scheduling algorithm) which adds the process of dealing with soft real-time applications is proposed. Finally, we verify real-time scheduling mechanism from two aspects of theory and experiment. The results indicate that our scheduling mechanism can achieve the following objectives. (1) It can reflect the difference of priority when scheduling hard and soft real-time applications. (2) It can ensure schedulability of hard real-time applications, that is, their rate of missing deadline is 0. (3) The overall rate of missing deadline of soft real-time applications can be less than 1. (4) The deadline of a non-real-time application is not set, whereas the scheduling algorithm that server 0 S uses can avoid the “starvation" of jobs and increase QOS. By doing that, our scheduling mechanism is more compatible with different types of applications and it will be applied more widely.

Keywords: Hard real-time, two-level scheduling profile, open real-time system, non-distinctive schedule, soft real-time

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6464 Gabriel-constrained Parametric Surface Triangulation

Authors: Oscar E. Ruiz, Carlos Cadavid, Juan G. Lalinde, Ricardo Serrano, Guillermo Peris-Fajarnes

Abstract:

The Boundary Representation of a 3D manifold contains FACES (connected subsets of a parametric surface S : R2 -! R3). In many science and engineering applications it is cumbersome and algebraically difficult to deal with the polynomial set and constraints (LOOPs) representing the FACE. Because of this reason, a Piecewise Linear (PL) approximation of the FACE is needed, which is usually represented in terms of triangles (i.e. 2-simplices). Solving the problem of FACE triangulation requires producing quality triangles which are: (i) independent of the arguments of S, (ii) sensitive to the local curvatures, and (iii) compliant with the boundaries of the FACE and (iv) topologically compatible with the triangles of the neighboring FACEs. In the existing literature there are no guarantees for the point (iii). This article contributes to the topic of triangulations conforming to the boundaries of the FACE by applying the concept of parameterindependent Gabriel complex, which improves the correctness of the triangulation regarding aspects (iii) and (iv). In addition, the article applies the geometric concept of tangent ball to a surface at a point to address points (i) and (ii). Additional research is needed in algorithms that (i) take advantage of the concepts presented in the heuristic algorithm proposed and (ii) can be proved correct.

Keywords: surface triangulation, conforming triangulation, surfacesampling, Gabriel complex.

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6463 Existence and Uniqueness of Periodic Solution for a Discrete-time SIR Epidemic Model with Time Delays and Impulses

Authors: Ling Liu, Yuan Ye

Abstract:

In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.

Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.

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6462 Optimizing the Project Delivery Time with Time Cost Trade-offs

Authors: Wei Lo, Ming-En Kuo

Abstract:

While to minimize the overall project cost is always one of the objectives of construction managers, to obtain the maximum economic return is definitely one the ultimate goals of the project investors. As there is a trade-off relationship between the project time and cost, and the project delivery time directly affects the timing of economic recovery of an investment project, to provide a method that can quantify the relationship between the project delivery time and cost, and identify the optimal delivery time to maximize economic return has always been the focus of researchers and industrial practitioners. Using genetic algorithms, this study introduces an optimization model that can quantify the relationship between the project delivery time and cost and furthermore, determine the optimal delivery time to maximize the economic return of the project. The results provide objective quantification for accurately evaluating the project delivery time and cost, and facilitate the analysis of the economic return of a project.

Keywords: Time-Cost Trade-Off, Genetic Algorithms, Resource Integration, Economic return.

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6461 Stability Analysis of Mutualism Population Model with Time Delay

Authors: Rusliza Ahmad, Harun Budin

Abstract:

This paper studies the effect of time delay on stability of mutualism population model with limited resources for both species. First, the stability of the model without time delay is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. We analyze the effect of time delay on the stability of the stable equilibrium point. Result showed that the time delay can induce instability of the stable equilibrium point, bifurcation and stability switches.

Keywords: Bifurcation, Delay margin, Mutualism population model, Time delay

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6460 Genetic Algorithms Multi-Objective Model for Project Scheduling

Authors: Elsheikh Asser

Abstract:

Time and cost are the main goals of the construction project management. The first schedule developed may not be a suitable schedule for beginning or completing the project to achieve the target completion time at a minimum total cost. In general, there are trade-offs between time and cost (TCT) to complete the activities of a project. This research presents genetic algorithms (GAs) multiobjective model for project scheduling considering different scenarios such as least cost, least time, and target time.

Keywords: Genetic algorithms, Time-cost trade-off.

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6459 Real-Time 3D City Generation using Shape Grammars with LOD Variations

Authors: Pearl Goswell, Jun Jo

Abstract:

Creating3D environments, including characters and cities, is a significantly time consuming process due to a large amount of workinvolved in designing and modelling.There have been a number of attempts to automatically generate 3D objects employing shape grammars. However it is still too early to apply the mechanism to real problems such as real-time computer games.The purpose of this research is to introduce a time efficient and cost effective method to automatically generatevarious 3D objects for real-time 3D games. This Shape grammar-based real-time City Generation (RCG) model is a conceptual model for generating 3Denvironments in real-time and can be applied to 3D gamesoranimations. The RCG system can generate even a large cityby applying fundamental principles of shape grammars to building elementsin various levels of detailin real-time.

Keywords: real-time city generation, shape grammars, 3D games, 3D modelling.

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6458 GenCos- Optimal Bidding Strategy Considering Market Power and Transmission Constraints: A Cournot-based Model

Authors: A. Badri

Abstract:

Restructured electricity markets may provide opportunities for producers to exercise market power maintaining prices in excess of competitive levels. In this paper an oligopolistic market is presented that all Generation Companies (GenCos) bid in a Cournot model. Genetic algorithm (GA) is applied to obtain generation scheduling of each GenCo as well as hourly market clearing prices (MCP). In order to consider network constraints a multiperiod framework is presented to simulate market clearing mechanism in which the behaviors of market participants are modelled through piecewise block curves. A mixed integer linear programming (MILP) is employed to solve the problem. Impacts of market clearing process on participants- characteristic and final market prices are presented. Consequently, a novel multi-objective model is addressed for security constrained optimal bidding strategy of GenCos. The capability of price-maker GenCos to alter MCP is evaluated through introducing an effective-supply curve. In addition, the impact of exercising market power on the variation of market characteristics as well as GenCos scheduling is studied.

Keywords: Optimal bidding strategy, Cournot equilibrium, market power, network constraints, market auction mechanism

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6457 A DEA Model for Performance Evaluation in The Presence of Time Lag Effect

Authors: Yanshuang Zhang, Byungho Jeong

Abstract:

Data Envelopment Analysis (DEA) is a methodology that computes efficiency values for decision making units (DMU) in a given period by comparing the outputs with the inputs. In many cases, there are some time lag between the consumption of inputs and the production of outputs. For a long-term research project, it is hard to avoid the production lead time phenomenon. This time lag effect should be considered in evaluating the performance of organizations. This paper suggests a model to calculate efficiency values for the performance evaluation problem with time lag. In the experimental part, the proposed methods are compared with the CCR and an existing time lag model using the data set of the 21st century frontier R&D program which is a long-term national R&D program of Korea.

Keywords: DEA, Efficiency, Time Lag

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6456 Forecasting Enrollment Model Based on First-Order Fuzzy Time Series

Authors: Melike Şah, Konstantin Y.Degtiarev

Abstract:

This paper proposes a novel improvement of forecasting approach based on using time-invariant fuzzy time series. In contrast to traditional forecasting methods, fuzzy time series can be also applied to problems, in which historical data are linguistic values. It is shown that proposed time-invariant method improves the performance of forecasting process. Further, the effect of using different number of fuzzy sets is tested as well. As with the most of cited papers, historical enrollment of the University of Alabama is used in this study to illustrate the forecasting process. Subsequently, the performance of the proposed method is compared with existing fuzzy time series time-invariant models based on forecasting accuracy. It reveals a certain performance superiority of the proposed method over methods described in the literature.

Keywords: Forecasting, fuzzy time series, linguistic values, student enrollment, time-invariant model.

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6455 Coding Structures for Seated Row Simulation of an Active Controlled Vibration Isolation and Stabilization System for Astronaut’s Exercise Platform

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

Abstract:

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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6454 Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay

Authors: Liqiong Liu, Shouming Zhong

Abstract:

In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.

Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality.

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6453 Surgery Scheduling Using Simulation with Arena

Authors: J. A. López, C.I. López, J.E. Olguín, C. Camargo, J. M. López

Abstract:

The institutions seek to improve their performance and quality of service, so that their patients are satisfied. This research project aims, conduct a time study program in the area of gynecological surgery, to determine the current level of capacity and optimize the programming time in order to adequately respond to demand. The system is analyzed by waiting lines and uses the simulation using ARENA to evaluate proposals for improvement and optimization programming time each of the surgeries.

Keywords: Time study, waiting lines, reducing time, simulation.

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6452 Does Leisure Time Use Contribute to a Wage Increase of the Thai People?

Authors: Siriwan Saksiriruthai

Abstract:

This paper develops models to analyze the relationship between leisure time and wage change. Using Thailand-s Time Use Survey and Labor Force Survey data, the estimation of wage changes in response to leisure time change indicates that media receiving, personal care and social participation and volunteer activities are the ones that significantly raise hourly wages. Thus, the finding suggests the stimulation in time use for media access to enhance knowledge and productivity, personal care for attractiveness and healthiness in order to raise productivity, and social activities to develop connections for possible future opportunities including wage increase. These activities should be promoted for productive leisure time and for welfare improvement.

Keywords: Leisure, wage, time use, Thailand.

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6451 Finite Time Symplectic Synchronization between Two Different Chaotic Systems

Authors: Chunming Xu

Abstract:

In this paper, the finite-time symplectic synchronization between two different chaotic systems is investigated. Based on the finite-time stability theory, a simple adaptive feedback scheme is proposed to realize finite-time symplectic synchronization for the Lorenz and L¨u systems. Numerical examples are provided to show the effectiveness of the proposed method.

Keywords: Chaotic systems, symplectic synchronization, finite-time synchronization, adaptive controller.

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6450 Discovery of Time Series Event Patterns based on Time Constraints from Textual Data

Authors: Shigeaki Sakurai, Ken Ueno, Ryohei Orihara

Abstract:

This paper proposes a method that discovers time series event patterns from textual data with time information. The patterns are composed of sequences of events and each event is extracted from the textual data, where an event is characteristic content included in the textual data such as a company name, an action, and an impression of a customer. The method introduces 7 types of time constraints based on the analysis of the textual data. The method also evaluates these constraints when the frequency of a time series event pattern is calculated. We can flexibly define the time constraints for interesting combinations of events and can discover valid time series event patterns which satisfy these conditions. The paper applies the method to daily business reports collected by a sales force automation system and verifies its effectiveness through numerical experiments.

Keywords: Text mining, sequential mining, time constraints, daily business reports.

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6449 Effects of Sowing Time on Yield and Oil Content of Different Sunflower Genotypes in Years with Different Water Supply

Authors: A. Novák, K. Máriás

Abstract:

We examined the effects of the sowing time on the yield production and oil content of the sunflower hybrids in 2010 and 2012. The crop year and the sowing time had both a strong impact on the yield, on the oil- content and yield. By delaying the sowing time both the yield crop result and the oil yield increased. In 2010 in terms of crop yield and oil yield results PR64H42 was the best, in 2012 NK Neoma, in all three sowing times. The oil content of the hybrids was better in 2010. The highest oil content was recorded at early sowing time. We found out that the hybrid had a stronger impact in 2010 on both crop yield result and on oil content than in 2012. The sowing time played a bigger role regarding yield results in 2012. In addition the sowing time influenced oil content development highly.

Keywords: Genotypes, oil content, sowing time, sunflower, yield.

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6448 Universal Qibla and Prayer Time Finder

Authors: M. Z. Ibrahim, M. Z. Norashikin

Abstract:

People nowadays love to travel around the world. Regardless of their location and time, they especially Muslims still need to perform their five times prayer. Normally for travelers, they need to bring maps, compass and for Muslim, they even have to bring Qibla pointer when they travel. It is slightly difficult to determine the Qibla direction and to know the time for each prayer. In this paper we present a new electronic device called Universal Qibla and Prayer Time Finder to locate the Qibla direction and to determine each prayer time based on the current user-s location. This device use PIC microcontroller equipped with digital compass and Global Positioning System (GPS) where it will display the exact Qibla direction and prayer time automatically at any place in the world. This device is reliable, user friendly and accurate in determining the Qibla direction and prayer time.

Keywords: Digital compass, embedded system, global position system, prayer time, qibla

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6447 Sensitivity Analysis of Real-Time Systems

Authors: Benjamin Gorry, Andrew Ireland, Peter King

Abstract:

Verification of real-time software systems can be expensive in terms of time and resources. Testing is the main method of proving correctness but has been shown to be a long and time consuming process. Everyday engineers are usually unwilling to adopt formal approaches to correctness because of the overhead associated with developing their knowledge of such techniques. Performance modelling techniques allow systems to be evaluated with respect to timing constraints. This paper describes PARTES, a framework which guides the extraction of performance models from programs written in an annotated subset of C.

Keywords: Performance Modelling, Real-time, SensitivityAnalysis.

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6446 Circadian Clock and Subjective Time Perception: A Simple Open Source Application for the Analysis of Induced Time Perception in Humans

Authors: Agata M. Kołodziejczyk, Mateusz Harasymczuk, Pierre-Yves Girardin, Lucie Davidová

Abstract:

Subjective time perception implies connection to cognitive functions, attention, memory and awareness, but a little is known about connections with homeostatic states of the body coordinated by circadian clock. In this paper, we present results from experimental study of subjective time perception in volunteers performing physical activity on treadmill in various phases of their circadian rhythms. Subjects were exposed to several time illusions simulated by programmed timing systems. This study brings better understanding for further improvement of of work quality in isolated areas. 

Keywords: Biological clock, light, time illusions, treadmill.

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6445 A Dual Model for Efficiency Evaluation Considering Time Lag Effect

Authors: Yan Shuang Zhang, Taehan Lee, Byung Ho Jeong

Abstract:

A DEA model can generally evaluate the performance using multiple inputs and outputs for the same period. However, it is hard to avoid the production lead time phenomenon some times, such as long-term project or marketing activity. A couple of models have been suggested to capture this time lag issue in the context of DEA. This paper develops a dual-MPO model to deal with time lag effect in evaluating efficiency. A numerical example is also given to show that the proposed model can be used to get efficiency and reference set of inefficient DMUs and to obtain projected target value of input attributes for inefficient DMUs to be efficient.

Keywords: DEA, efficiency, time lag, dual problem.

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