Search results for: Adaptive nonlinear control

Authors: Shuo-Li Hsu, Peng-Wei Gau, I-Lin Wu, Jyh-Horng Jeng

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For most image fusion algorithms separate relationship by pixels in the image and treat them more or less independently. In addition, they have to be adjusted different parameters in different time or weather. In this paper, we propose a region–based image fusion which combines aspects of feature and pixel-level fusion method to replace only by pixel. The basic idea is to segment far infrared image only and to add information of each region from segmented image to visual image respectively. Then we determine different fused parameters according different region. At last, we adopt artificial neural network to deal with the problems of different time or weather, because the relationship between fused parameters and image features are nonlinear. It render the fused parameters can be produce automatically according different states. The experimental results present the method we proposed indeed have good adaptive capacity with automatic determined fused parameters. And the architecture can be used for lots of applications.

Keywords: Image fusion, Region-based fusion, Segmentation, Neural network, Multi-sensor.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

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In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: A. K. Kamath, N. M. Singh, R. Pasumarthy

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This paper investigates the control of a bouncing ball using Model Predictive Control. Bouncing ball is a benchmark problem for various rhythmic tasks such as juggling, walking, hopping and running. Humans develop intentions which may be perceived as our reference trajectory and tries to track it. The human brain optimizes the control effort needed to track its reference; this forms the central theme for control of bouncing ball in our investigations.

Keywords: Bouncing Ball, impact dynamics, intermittent control, model predictive control.

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Authors: J. Hossen, A. Rahman, K. Samsudin, F. Rokhani, S. Sayeed, R. Hasan

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The Neuro-Fuzzy hybridization scheme has become of research interest in pattern classification over the past decade. The present paper proposes a novel Modified Adaptive Fuzzy Inference Engine (MAFIE) for pattern classification. A modified Apriori algorithm technique is utilized to reduce a minimal set of decision rules based on input output data sets. A TSK type fuzzy inference system is constructed by the automatic generation of membership functions and rules by the fuzzy c-means clustering and Apriori algorithm technique, respectively. The generated adaptive fuzzy inference engine is adjusted by the least-squares fit and a conjugate gradient descent algorithm towards better performance with a minimal set of rules. The proposed MAFIE is able to reduce the number of rules which increases exponentially when more input variables are involved. The performance of the proposed MAFIE is compared with other existing applications of pattern classification schemes using Fisher-s Iris and Wisconsin breast cancer data sets and shown to be very competitive.

Keywords: Apriori algorithm, Fuzzy C-means, MAFIE, TSK

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Authors: Yong-can Cao, Wei-dong Zhang

Abstract:

To deal with random delays in Networked Control System (NCS), Modified Fuzzy PID Controller is introduced in this paper to implement real-time control adaptively. Via adjusting the control signal dynamically, the system performance is improved. In this paper, the design process and the ultimate simulation results are represented. Finally, examples and corresponding comparisons prove the significance of this method.

Keywords: Fuzzy Control, Networked Control System, PID, Random Delays

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Authors: Javed Khan, Aamir Saeed Malik, Nidal Kamel, Sarat Chandra Dass, Azura Mohd Affandi

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Low contrast images can result from the wrong setting of image acquisition or poor illumination conditions. Such images may not be visually appealing and can be difficult for feature extraction. Contrast enhancement of color images can be useful in medical area for visual inspection. In this paper, a new technique is proposed to improve the contrast of color images. The RGB (red, green, blue) color image is transformed into normalized RGB color space. Adaptive histogram equalization technique is applied to each of the three channels of normalized RGB color space. The corresponding channels in the original image (low contrast) and that of contrast enhanced image with adaptive histogram equalization (AHE) are morphed together in proper proportions. The proposed technique is tested on seventy color images of acne patients. The results of the proposed technique are analyzed using cumulative variance and contrast improvement factor measures. The results are also compared with decorrelation stretch. Both subjective and quantitative analysis demonstrates that the proposed techniques outperform the other techniques.

Keywords: Contrast enhancement, normalized RGB, adaptive histogram equalization, cumulative variance.

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

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In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: Ilqar Ramazanli

Abstract:

The matrix completion problem has been studied broadly under many underlying conditions. In many real-life scenarios, we could expect elements from distinct columns or distinct positions to have a different cost. In this paper, we explore this generalization under adaptive conditions. We approach the problem under two different cost models. The first one is that entries from different columns have different observation costs, but, within the same column, each entry has a uniform cost. The second one is any two entry has different observation cost, despite being the same or different columns. We provide complexity analysis of our algorithms and provide tightness guarantees.

Keywords: Matrix completion, adaptive learning, heterogeneous cost, Matroid optimization.

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Authors: Amir Rastegarnia, Mohammad Ali Tinati, Azam Khalili

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In this paper we consider the problem of distributed adaptive estimation in wireless sensor networks for two different observation noise conditions. In the first case, we assume that there are some sensors with high observation noise variance (noisy sensors) in the network. In the second case, different variance for observation noise is assumed among the sensors which is more close to real scenario. In both cases, an initial estimate of each sensor-s observation noise is obtained. For the first case, we show that when there are such sensors in the network, the performance of conventional distributed adaptive estimation algorithms such as incremental distributed least mean square (IDLMS) algorithm drastically decreases. In addition, detecting and ignoring these sensors leads to a better performance in a sense of estimation. In the next step, we propose a simple algorithm to detect theses noisy sensors and modify the IDLMS algorithm to deal with noisy sensors. For the second case, we propose a new algorithm in which the step-size parameter is adjusted for each sensor according to its observation noise variance. As the simulation results show, the proposed methods outperforms the IDLMS algorithm in the same condition.

Keywords: Distributes estimation, sensor networks, adaptive filter, IDLMS.

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Authors: An Hong Nguyen, Chatpan Chintanapakdee, Toshiro Hayashikawa

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Presented herein is an assessment of current nonlinear static procedures (NSPs) for seismic evaluation of bucklingrestrained braced frames (BRBFs) which have become a favorable lateral-force resisting system for earthquake resistant buildings. The bias and accuracy of modal, improved modal pushover analysis (MPA, IMPA) and mass proportional pushover (MPP) procedures are comparatively investigated when they are applied to BRBF buildings subjected to two sets of strong ground motions. The assessment is based on a comparison of seismic displacement demands such as target roof displacements, peak floor/roof displacements and inter-story drifts. The NSP estimates are compared to 'exact' results from nonlinear response history analysis (NLRHA). The response statistics presented show that the MPP procedure tends to significantly overestimate seismic demands of lower stories of tall buildings considered in this study while MPA and IMPA procedures provide reasonably accurate results in estimating maximum inter-story drift over all stories of studied BRBF systems.

Keywords: Buckling-restrained braced frames, nonlinearresponse history analysis, nonlinear static procedure, seismicdemands.

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Authors: Gilberto Gonzalez-A

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Bond graph models of an electrical transformer including the nonlinear saturation are presented. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two and three windings using the properties of a bond graph. The modelling and analysis using this methodology to three phase power transformers or transformers with internal incipient faults can be extended.

Keywords: Bond graph, electrical transformer, nonlinear saturation

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

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In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: Performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover.

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Authors: Surbhi Gupta, Alka Handa, Parvinder S.Sandhu

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Stegnography is a new way of secret communication the most widely used mechanism on account of its simplicity is the use of the least significant bit. We have used the least significant bit (2 LSB and 4 LSB) substitution method. Depending upon the characteristics of the individual portions of cover image we decide whether to use 2 LSB or 4 LSB thus it is an adaptive stegnography technique. We used one of the three channels to behave as indicator to indicate the presence of hidden data in other two channels. The module showed impressive results in terms of capacity to hide the data. In proposed method, instead of using RGB color space directly, YCbCr color space is used to make use of human visual system characteristic.

Keywords: Stegoimage, steganography, Pixel indicator, segmentation, YCbCr..

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Authors: S. Dhahri, A. Zitouni, H. Chaouch, R. Tourki

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This paper presents an adaptive motion estimator that can be dynamically reconfigured by the best algorithm depending on the variation of the video nature during the lifetime of an application under running. The 4 Step Search (4SS) and the Gradient Search (GS) algorithms are integrated in the estimator in order to be used in the case of rapid and slow video sequences respectively. The Full Search Block Matching (FSBM) algorithm has been also integrated in order to be used in the case of the video sequences which are not real time oriented. In order to efficiently reduce the computational cost while achieving better visual quality with low cost power, the proposed motion estimator is based on a Variable Block Size (VBS) scheme that uses only the 16x16, 16x8, 8x16 and 8x8 modes. Experimental results show that the adaptive motion estimator allows better results in term of Peak Signal to Noise Ratio (PSNR), computational cost, FPGA occupied area, and dissipated power relatively to the most popular variable block size schemes presented in the literature.

Keywords: H264, Configurable Motion Estimator, VariableBlock Size, PSNR, Dissipated power.

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Authors: A. Javed, K. Djidjeli, J. T. Xing

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The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not distributed uniformly throughout the domain. Unlike conventional approaches which assume globally similar values of RBF shape parameters, the presented ASP technique suggests that shape parameter be calculated exclusively for each data point (or node) based on the distribution of data points within its own influence domain. This will ensure interpolation accuracy while still maintaining well conditioned system of equations for RBF weights. Performance and accuracy of ASP technique has been tested by evaluating derivatives and laplacian of a known function using RBF in Finite difference mode (RBFFD), with and without the use of adaptivity in shape parameters. Application of adaptive shape parameters (ASP) for solution of incompressible Navier Strokes equations has been presented by solving lid driven cavity flow problem on mesh-free domain using RBF-FD. The results have been compared for fixed and adaptive shape parameters. Improved accuracy has been achieved with the use of ASP in RBF-FD especially at regions where larger gradients of field variables exist.

Keywords: CFD, Meshless Particle Method, Radial Basis Functions, Shape Parameters

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Authors: M. M. Rahman

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The present contribution deals with the thermophoretic deposition of nanoparticles over a rapidly rotating permeable disk in the presence of partial slip, magnetic field, thermal radiation, thermal-diffusion, and diffusion-thermo effects. The governing nonlinear partial differential equations such as continuity, momentum, energy and concentration are transformed into nonlinear ordinary differential equations using similarity analysis, and the solutions are obtained through the very efficient computer algebra software MATLAB. Graphical results for non-dimensional concentration and temperature profiles including thermophoretic deposition velocity and Stanton number (thermophoretic deposition flux) in tabular forms are presented for a range of values of the parameters characterizing the flow field. It is observed that slip mechanism, thermal-diffusion, diffusion-thermo, magnetic field and radiation significantly control the thermophoretic particles deposition rate. The obtained results may be useful to many industrial and engineering applications.

Keywords: Boundary layer flows, convection, diffusion-thermo, rotating disk, thermal-diffusion, thermophoresis.

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Authors: Halim Djerroud, Arab Ali Cherif

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We assume that conscious functions are implemented automatically. In other words that consciousness as well as the non-consciousness aspect of human thought, planning and perception, are produced by biologically adaptive algorithms. We propose that the mechanisms of consciousness can be produced using similar adaptive algorithms to those executed by the mechanism. In this paper, we present a computational model of consciousness, the ”Global Abstraction Workspace” which is an internal environmental modelling perceived as a multi-agent system. This system is able to evolve and generate new data and processes as well as actions in the environment.

Keywords: Artificial consciousness, cognitive architecture, global abstraction workspace, mutli-agents system.

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Authors: Grzegorz Ulacha, Ryszard Stasiński

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In the paper an effective context based lossless coding technique is presented. Three principal and few auxiliary contexts are defined. The predictor adaptation technique is an improved CoBALP algorithm, denoted CoBALP+. Cumulated predictor error combining 8 bias estimators is calculated. It is shown experimentally that indeed, the new technique is time-effective while it outperforms the well known methods having reasonable time complexity, and is inferior only to extremely computationally complex ones.

Keywords: Adaptive prediction, context coding, image losslesscoding, prediction error bias correction.

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Authors: Fouad Salha , X. Guillaud

Abstract:

Directional over current relays (DOCR) are commonly used in power system protection as a primary protection in distribution and sub-transmission electrical systems and as a secondary protection in transmission systems. Coordination of protective relays is necessary to obtain selective tripping. In this paper, an approach for efficiency reduction of DOCRs nonlinear optimum coordination (OC) is proposed. This was achieved by modifying the objective function and relaxing several constraints depending on the four constraints classification, non-valid, redundant, pre-obtained and valid constraints. According to this classification, the far end fault effect on the objective function and constraints, and in consequently on relay operating time, was studied. The study was carried out, firstly by taking into account the near-end and far-end faults in DOCRs coordination problem formulation; and then faults very close to the primary relays (nearend faults). The optimal coordination (OC) was achieved by simultaneously optimizing all variables (TDS and Ip) in nonlinear environment by using of Genetic algorithm nonlinear programming techniques. The results application of the above two approaches on 6-bus and 26-bus system verify that the far-end faults consideration on OC problem formulation don-t lose the optimality.

Keywords: Backup/Primary relay, Coordination time interval (CTI), directional over current relays, Genetic algorithm, time dial setting (TDS), pickup current setting (Ip), nonlinear programming.

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

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Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: Mohd Fikri Azli bin Abdullah, Khairul Anwar bin Kamarul Hatta, Esther Jeganathan

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WiFi has become an essential technology that is widely used nowadays. It is famous due to its convenience to be used with mobile devices. This is especially true for Internet users worldwide that use WiFi connections. There are many location based services that are available nowadays which uses Wireless Fidelity (WiFi) signal fingerprinting. A common example that is gaining popularity in this era would be Foursquare. In this work, the WiFi signal would be used to estimate the user or client’s location. Similar to GPS, fingerprinting method needs a floor plan to increase the accuracy of location estimation. Still, the factor of inconsistent WiFi signal makes the estimation defer at different time intervals. Given so, an adaptive method is needed to obtain the most accurate signal at all times. WiFi signals are heavily distorted by external factors such as physical objects, radio frequency interference, electrical interference, and environmental factors to name a few. Due to these factors, this work uses a method of reducing the signal noise and estimation using the Nearest Neighbour based on past activities of the signal to increase the signal accuracy up to more than 80%. The repository yet increases the accuracy by using Artificial Neural Network (ANN) pattern matching. The repository acts as the server cum support of the client side application decision. Numerous previous works has adapted the methods of collecting signal strengths in the repository over the years, but mostly were just static. In this work, proposed solutions on how the adaptive method is done to match the signal received to the data in the repository are highlighted. With the said approach, location estimation can be done more accurately. Adaptive update allows the latest location fingerprint to be stored in the repository. Furthermore, any redundant location fingerprints are removed and only the updated version of the fingerprint is stored in the repository. How the location estimation of the user can be predicted would be highlighted more in the proposed solution section. After some studies on previous works, it is found that the Artificial Neural Network is the most feasible method to deploy in updating the repository and making it adaptive. The Artificial Neural Network functions are to do the pattern matching of the WiFi signal to the existing data available in the repository.

Keywords: Adaptive Repository, Artificial Neural Network, Location Estimation, Nearest Neighbour Euclidean Distance, WiFi RSSI Fingerprinting.

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Authors: Péter Restás, Andrea Czibor, Zsolt Péter Szabó

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Purpose: This article aims to rethink the phenomena of employee behavior as a product of a system. Both organizational culture and Complex Adaptive Systems (CAS) theory emphasize that individual behavior depends on the specific system and the unique organizational culture. These two major theories are both represented in the field of organizational studies; however, they are rarely used together for the comprehensive understanding of workplace behavior. Methodology: By reviewing the literature we use key concepts stemming from organizational culture and CAS theory in order to show the similarities between these theories and create an enriched understanding of employee behavior. Findings: a) Workplace behavior is defined here as social cognition issue. b) Organizations are discussed here as complex systems, and cultures which drive and dictate the cognitive processes of agents in the system. c) Culture gives CAS theory a context which lets us see organizations not just as ever-changing and unpredictable, but as such systems that aim to create and maintain stability by recurring behavior. Conclusion: Applying the knowledge from culture and CAS theory sheds light on our present understanding of employee behavior, also emphasizes the importance of novel ways in organizational research and management.

Keywords: Complex adaptive systems theory, employee behavior, organizational culture, stability.

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well known formulas.

Keywords: Conjugate gradient method, conjugate gradient coefficient, global convergence.

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Authors: M. Chaoui, M-T. Laskri

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The evolution of information and communication technology has made a very powerful support for the improvement of online learning platforms in creation of courses. This paper presents a study that attempts to explore new web architecture for creating an adaptive online learning system to profiles of learners, using the Web as a source for the automatic creation of courses for the online training platform. This architecture will reduce the time and decrease the effort performed by the drafters of the current e-learning platform, and direct adaptation of the Web content will greatly enrich the quality of online training courses.

Keywords: Web Content, e-Learning, Educational Content, LMS, Profiles of Learners

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Authors: Ling Liu, Yuan Ye

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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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Authors: Hyun-Chool Shin

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In this paper we propose a simple adaptive algorithm iteratively solving the unit-norm constrained optimization problem. Instead of conventional parameter norm based normalization, the proposed algorithm incorporates scalar normalization which is computationally much simpler. The analysis of stationary point is presented to show that the proposed algorithm indeed solves the constrained optimization problem. The simulation results illustrate that the proposed algorithm performs as good as conventional ones while being computationally simpler.

Keywords: constrained optimization, unit-norm, LMS, principle component analysis.

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Authors: Fooad Karimi Ghaleh Jough, Mohsen Soori

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Today, the occurrence of progressive failure in structures has become a challenging issue, requiring the presentation of suitable solutions for structural resistance to this phenomenon. It is also necessary to evaluate the vulnerability of existing and under-construction buildings to progressive failure. The kind of lateral load-resisting system the building and its connections have is one of the most significant and influential variables in structural resistance to the risk of progressing failure. Using the "Alternative Path" approach suggested by the GSA2003 and UFC2013 recommendations, different configurations of semi-rigid connections against progressive failure are offered in this study. In order to do this, the Opensees program was used to model nine distinct semi-rigid connection configurations on a three-story Special Area of Conservation (SAC) structure, accounting for the impact of connection stiffness. Then, using nonlinear dynamic analysis, the effects of column removal were explored in two scenarios: corner column removal and middle column removal on the first level. Nonlinear static analysis results showed that when a column is removed, structures with semi-rigid connections experience larger displacements, which result in the construction of a plastic hinge. Furthermore, it was clear from the findings of the nonlinear static analysis that the possibility of progressive failure increased with the number of semi-rigid connections in the structure.

Keywords: Semi-rigid, nonlinear static analysis, progressive collapse, alternative path.

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Authors: R.Balamurugan, S.Subramanian

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This paper presents the solution of power economic dispatch (PED) problem of generating units with valve point effects and multiple fuel options using Self-Adaptive Differential Evolution (SDE) algorithm. The global optimal solution by mathematical approaches becomes difficult for the realistic PED problem in power systems. The Differential Evolution (DE) algorithm is found to be a powerful evolutionary algorithm for global optimization in many real problems. In this paper the key parameters of control in DE algorithm such as the crossover constant CR and weight applied to random differential F are self-adapted. The PED problem formulation takes into consideration of nonsmooth fuel cost function due to valve point effects and multi fuel options of generator. The proposed approach has been examined and tested with the numerical results of PED problems with thirteen-generation units including valve-point effects, ten-generation units with multiple fuel options neglecting valve-point effects and ten-generation units including valve-point effects and multiple fuel options. The test results are promising and show the effectiveness of proposed approach for solving PED problems.

Keywords: Multiple fuels, power economic dispatch, selfadaptivedifferential evolution and valve-point effects.

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Authors: Muhammad Rehan Khalid, Muhammad Haroon Siddiqui, Danish Ilyas

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This paper explores the implementation of adaptive coding and modulation schemes for Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) feedback systems. Adaptive coding and modulation enables robust and spectrally-efficient transmission over time-varying channels. The basic premise is to estimate the channel at the receiver and feed this estimate back to the transmitter, so that the transmission scheme can be adapted relative to the channel characteristics. Two types of codebook based channel feedback techniques are used in this work. The longterm and short-term CSI at the transmitter is used for efficient channel utilization. OFDM is a powerful technique employed in communication systems suffering from frequency selectivity. Combined with multiple antennas at the transmitter and receiver, OFDM proves to be robust against delay spread. Moreover, it leads to significant data rates with improved bit error performance over links having only a single antenna at both the transmitter and receiver. The coded modulation increases the effective transmit power relative to uncoded variablerate variable-power MQAM performance for MIMO-OFDM feedback system. Hence proposed arrangement becomes an attractive approach to achieve enhanced spectral efficiency and improved error rate performance for next generation high speed wireless communication systems.

Keywords: Adaptive Coded Modulation, MQAM, MIMO, OFDM, Codebooks, Feedback.

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Authors: Daniela Elena Marinescu, Ioana Manafi, Dumitru Marin

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We consider a Principal-Agent model with the Principal being a seller who does not know perfectly how much the buyer (the Agent) is willing to pay for the good. The buyer-s preferences are hence his private information. The model corresponds to the nonlinear pricing problem of Maskin and Riley. We assume there are three types of Agents. The model is solved using “informational rents" as variables. In the last section we present the main characteristics of the optimal contracts in asymmetric information and some possible extensions of the model.

Keywords: Adverse selection, asymmetric information, informational rent, nonlinear pricing, optimal contract

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