Search results for: human approximation
8527 Approximation Algorithms for Peak-Demand Reduction
Authors: Zaid Jamal Saeed Almahmoud
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Smart grid is emerging as the future power grid, with smart techniques to optimize power consumption and electricity generation. Minimizing peak power consumption under a fixed delay requirement is a significant problem in the smart grid.For this problem, all appliances must be scheduled within a given finite time duration. We consider the problem of minimizing the peak demand under appliances constraints by scheduling power jobs with uniform release dates and deadlines. As the problem is known to be NP-hard, we analyze the performance of a version of the natural greedy heuristic for solving this problem. Our theoretical analysis and experimental results show that the proposed heuristic outperforms existing methods by providing a better approximation to the optimal solution.Keywords: peak demand scheduling, approximation algorithms, smart grid, heuristics
Procedia PDF Downloads 688526 Identification of Wiener Model Using Iterative Schemes
Authors: Vikram Saini, Lillie Dewan
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This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model
Procedia PDF Downloads 3668525 Human Security and Human Trafficking Related Corruption
Authors: Ekin D. Horzum
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The aim of the proposal is to examine the relationship between human trafficking related corruption and human security. The proposal suggests that the human trafficking related corruption is about willingness of the states to turn a blind eye to the human trafficking cases. Therefore, it is important to approach human trafficking related corruption in terms of human security and human rights violation to find an effective way to fight against human trafficking. In this context, the purpose of this proposal is to examine the human trafficking related corruption as a safe haven in which trafficking thrives for perpetrators.Keywords: human trafficking, human security, human rights, corruption, organized crime
Procedia PDF Downloads 4408524 Bivariate Generalization of q-α-Bernstein Polynomials
Authors: Tarul Garg, P. N. Agrawal
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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness
Procedia PDF Downloads 3558523 Random Walks and Option Pricing for European and American Options
Authors: Guillaume Leduc
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In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.Keywords: random walk approximation, European and American options, rate of convergence, option pricing
Procedia PDF Downloads 4318522 An Approximation of Daily Rainfall by Using a Pixel Value Data Approach
Authors: Sarisa Pinkham, Kanyarat Bussaban
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The research aims to approximate the amount of daily rainfall by using a pixel value data approach. The daily rainfall maps from the Thailand Meteorological Department in period of time from January to December 2013 were the data used in this study. The results showed that this approach can approximate the amount of daily rainfall with RMSE=3.343.Keywords: daily rainfall, image processing, approximation, pixel value data
Procedia PDF Downloads 3588521 Function Approximation with Radial Basis Function Neural Networks via FIR Filter
Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim
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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter
Procedia PDF Downloads 4328520 Influence of Glenohumeral Joint Approximation Technique on the Cardiovascular System in the Acute Phase after Stroke
Authors: Iva Hereitova, Miroslav Svatek, Vit Novacek
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Background and Aim: Autonomic imbalance is one of the complications for immobilized patients in the acute stage after a stroke. The predominance of sympathetic activity significantly increases cardiac activity. The technique of glenohumeral joint approximation may contribute in a non-pharmacological way to the regulation of blood pressure and heart rate in patients in this risk group. The aim of the study was to evaluate the effect of glenohumeral joint approximation on the change in heart rate and blood pressure in immobilized patients in the acute phase after a stroke. Methods: The experimental study bilaterally evaluated heart rate, systolic and diastolic pressure values before and after glenohumeral joint approximation in 40 immobilized participants (72.6 ± 10.2 years) in the acute phase after stroke. The experimental group was compared with 40 healthy participants in the control group (68.6 ± 14.2 years). An SpO2 vital signs monitor and a validated Microlife WatchBP Office blood pressure monitor were used for evaluation. Statistical processing and evaluation were performed in MATLAB R2019 (The Math Works®, Inc., Natick, MA, USA). Results: Approximation of the glenohumeral joint resulted in a statistically significant decrease in systolic and diastolic pressure. An average decrease in systolic pressure for individual groups ranged from 8.2 to 11.3 mmHg (p <0.001). For diastolic pressure, the average decrease ranged from 5.0 - 14.2 mmHg (p <0.001). There was a statistically significant reduction in heart rate (p <0.01) only in patients after ischemic stroke in the inferior cerebral artery. There was the average decrease in heart rate of 3.9 beats per minute (median 4 beats per minute). Conclusion: Approximation of the glenohumeral joint leads to a statistically significant decrease in systolic and diastolic pressure in immobilized patients in the acute phase after stroke.Keywords: Aproximation technique, Cardiovaskular system, Glenohumeral joint, Stroke
Procedia PDF Downloads 1808519 Comparison of Two Theories for the Critical Laser Radius in Thermal Quantum Plasma
Authors: Somaye Zare
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The critical beam radius is a significant factor that predicts the behavior of the laser beam in the plasma, so if the laser beam radius is adequately greater in comparison to it, the beam will experience stable focusing on the plasma; otherwise, the beam will diverge after entering into the plasma. In this work, considering the paraxial approximation and moment theories, the localization of a relativistic laser beam in thermal quantum plasma is investigated. Using the dielectric function obtained in the quantum hydrodynamic model, the mathematical equation for the laser beam width parameter is attained and solved numerically by the fourth-order Runge-Kutta method. The results demonstrate that the stouter focusing effect is occurred in the moment theory compared to the paraxial approximation. Besides, similar to the two theories, with increasing Fermi temperature, plasma density, and laser intensity, the oscillation rate of the beam width parameter growths and focusing length reduces which means improving the focusing effect. Furthermore, it is understood that behaviors of the critical laser radius are different in the two theories, in the paraxial approximation, the critical radius after a minimum value is enhanced with increasing laser intensity, but in the moment theory, with increasing laser intensity, the critical radius decreases until it becomes independent of the laser intensity.Keywords: laser localization, quantum plasma, paraxial approximation, moment theory, quantum hydrodynamic model
Procedia PDF Downloads 468518 Nonparametric Copula Approximations
Authors: Serge Provost, Yishan Zang
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Copulas are currently utilized in finance, reliability theory, machine learning, signal processing, geodesy, hydrology and biostatistics, among several other fields of scientific investigation. It follows from Sklar's theorem that the joint distribution function of a multidimensional random vector can be expressed in terms of its associated copula and marginals. Since marginal distributions can easily be determined by making use of a variety of techniques, we address the problem of securing the distribution of the copula. This will be done by using several approaches. For example, we will obtain bivariate least-squares approximations of the empirical copulas, modify the kernel density estimation technique and propose a criterion for selecting appropriate bandwidths, differentiate linearized empirical copulas, secure Bernstein polynomial approximations of suitable degrees, and apply a corollary to Sklar's result. Illustrative examples involving actual observations will be presented. The proposed methodologies will as well be applied to a sample generated from a known copula distribution in order to validate their effectiveness.Keywords: copulas, Bernstein polynomial approximation, least-squares polynomial approximation, kernel density estimation, density approximation
Procedia PDF Downloads 448517 Analytical Downlink Effective SINR Evaluation in LTE Networks
Authors: Marwane Ben Hcine, Ridha Bouallegue
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The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.Keywords: LTE, OFDMA, effective SINR, log skew normal approximation
Procedia PDF Downloads 3348516 Ab Initio Study of Structural, Elastic, Electronic and Thermal Properties of Full Heusler
Authors: M. Khalfa, H. Khachai, F. Chiker, K. Bougherara, R. Khenata, G. Murtaza, M. Harmel
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A theoretical study of structural, elastic, electronic and thermodynamic properties of Fe2VX, (with X = Al and Ga), were studied by means of the full-relativistic version of the full-potential augmented plane wave plus local orbitals method. For exchange and correlation potential we used both generalized-gradient approximation (GGA) and local-density approximation (LDA). Our calculated ground state properties like as lattice constants, bulk modulus and elastic constants appear more accurate when we employed the GGA rather than the LDA approximation, and these results agree very well with the available experimental and theoretical data. Further, prediction of the thermal effects on some macroscopic properties of Fe2VAl and Fe2VGa are given in this paper using the quasi-harmonic Debye model in which the lattice vibrations are taken into account. We have obtained successfully the variations of the primitive cell volume, volume expansion coefficient, heat capacities and Debye temperature with pressure and temperature in the ranges of 0–40 GPa and 0–1500 K.Keywords: full Heusler, FP-LAPW, electronic properties, thermal properties
Procedia PDF Downloads 4608515 The Impact of Artificial Intelligence on Human Rights Development
Authors: Kerols Seif Said Botros
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The relationship between development and human rights has been debated for a long time. Various principles, from the right to development to development-based human rights, are applied to understand the dynamics between these two concepts. Despite the measures calculated, the connection between enhancement and human rights remains vague. Despite, the connection between these two opinions and the need to strengthen human rights have increased in recent years. It will then be examined whether the right to sustainable development is acceptable or not. In various human rights instruments and this is a good vibe to the request cited above. The book then cites domestic and international human rights treaties, as well as jurisprudence and regulations defining human rights institutions, to support this view.Keywords: sustainable development, human rights, the right to development, the human rights-based approach to development, environmental rights, economic development, social sustainability human rights protection, human rights violations, workers’ rights, justice, security.
Procedia PDF Downloads 178514 Mathematical and Numerical Analysis of a Nonlinear Cross Diffusion System
Authors: Hassan Al Salman
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We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis
Procedia PDF Downloads 3598513 Condition for Plasma Instability and Stability Approaches
Authors: Ratna Sen
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As due to very high temperature of Plasma it is very difficult to confine it for sufficient time so that nuclear fusion reactions to take place, As we know Plasma escapes faster than the binary collision rates. We studied the ball analogy and the ‘energy principle’ and calculated the total potential energy for the whole Plasma. If δ ⃗w is negative, that is decrease in potential energy then the plasma will be unstable. We also discussed different approaches of stability analysis such as Nyquist Method, MHD approximation and Vlasov approach of plasma stability. So that by using magnetic field configurations we can able to create a stable Plasma in Tokamak for generating energy for future generations.Keywords: jello, magnetic field configuration, MHD approximation, energy principle
Procedia PDF Downloads 4138512 RAFU Functions in Robotics and Automation
Authors: Alicia C. Sanchez
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This paper investigates the implementation of RAFU functions (radical functions) in robotics and automation. Specifically, the main goal is to show how these functions may be useful in lane-keeping control and the lateral control of autonomous machines, vehicles, robots or the like. From the knowledge of several points of a certain route, the RAFU functions are used to achieve the lateral control purpose and maintain the lane-keeping errors within the fixed limits. The stability that these functions provide, their ease of approaching any continuous trajectory and the control of the possible error made on the approximation may be useful in practice.Keywords: automatic navigation control, lateral control, lane-keeping control, RAFU approximation
Procedia PDF Downloads 2578511 An Improved Prediction Model of Ozone Concentration Time Series Based on Chaotic Approach
Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani
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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.Keywords: chaotic approach, phase space, Cao method, local linear approximation method
Procedia PDF Downloads 3018510 Scaling Analysis for the Liquefaction Phenomena Generated by Water Waves
Authors: E. Arcos, E. Bautista, F. Méndez
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In this work, a scaling analysis of the liquefaction phenomena is presented. The characteristic scales are obtained by balancing term by term of the well-known partial dynamics governing equations, (U − P). From the above, the order of magnitude of the horizontal displacement is very smaller compared with the vertical displacement and therefore the governing equation is only a function of the dependent vertical variables. The U − P approximation is reduced and presented in its dimensionless version. This scaling analysis can be used to obtain analytical solutions of the liquefaction phenomena under the action of the water waves.Keywords: approximation U-P, porous seabed, scaling analysis, water waves
Procedia PDF Downloads 3238509 Atomistic Study of Structural and Phases Transition of TmAs Semiconductor, Using the FPLMTO Method
Authors: Rekab Djabri Hamza, Daoud Salah
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We report first-principles calculations of structural and magnetic properties of TmAs compound in zinc blende(B3) and CsCl(B2), structures employing the density functional theory (DFT) within the local density approximation (LDA). We use the full potential linear muffin-tin orbitals (FP-LMTO) as implemented in the LMTART-MINDLAB code (Calculation). Results are given for lattice parameters (a), bulk modulus (B), and its first derivatives(B’) in the different structures NaCl (B1) and CsCl (B2). The most important result in this work is the prediction of the possibility of transition; from cubic rocksalt (NaCl)→ CsCl (B2) (32.96GPa) for TmAs. These results use the LDA approximation.Keywords: LDA, phase transition, properties, DFT
Procedia PDF Downloads 868508 Approximation of Intersection Curves of Two Parametric Surfaces
Authors: Misbah Irshad, Faiza Sarfraz
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The problem of approximating surface to surface intersection is considered to be very important in computer aided geometric design and computer aided manufacturing. Although it is a complex problem to handle, its continuous need in the industry makes it an active topic in research. A technique for approximating intersection curves of two parametric surfaces is proposed, which extracts boundary points and turning points from a sequence of intersection points and interpolate them with the help of rational cubic spline functions. The proposed approach is demonstrated with the help of examples and analyzed by calculating error.Keywords: approximation, parametric surface, spline function, surface intersection
Procedia PDF Downloads 2368507 Shoreline Change Estimation from Survey Image Coordinates and Neural Network Approximation
Authors: Tienfuan Kerh, Hsienchang Lu, Rob Saunders
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Shoreline erosion problems caused by global warming and sea level rising may result in losing of land areas, so it should be examined regularly to reduce possible negative impacts. Initially in this study, three sets of survey images obtained from the years of 1990, 2001, and 2010, respectively, are digitalized by using graphical software to establish the spatial coordinates of six major beaches around the island of Taiwan. Then, by overlaying the known multi-period images, the change of shoreline can be observed from their distribution of coordinates. In addition, the neural network approximation is used to develop a model for predicting shoreline variation in the years of 2015 and 2020. The comparison results show that there is no significant change of total sandy area for all beaches in the three different periods. However, the prediction results show that two beaches may exhibit an increasing of total sandy areas under a statistical 95% confidence interval. The proposed method adopted in this study may be applicable to other shorelines of interest around the world.Keywords: digitalized shoreline coordinates, survey image overlaying, neural network approximation, total beach sandy areas
Procedia PDF Downloads 2508506 Error Estimation for the Reconstruction Algorithm with Fan Beam Geometry
Authors: Nirmal Yadav, Tanuja Srivastava
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Shannon theory is an exact method to recover a band limited signals from its sampled values in discrete implementation, using sinc interpolators. But sinc based results are not much satisfactory for band-limited calculations so that convolution with window function, having compact support, has been introduced. Convolution Backprojection algorithm with window function is an approximation algorithm. In this paper, the error has been calculated, arises due to this approximation nature of reconstruction algorithm. This result will be defined for fan beam projection data which is more faster than parallel beam projection.Keywords: computed tomography, convolution backprojection, radon transform, fan beam
Procedia PDF Downloads 4598505 Bayesian Using Markov Chain Monte Carlo and Lindley's Approximation Based on Type-I Censored Data
Authors: Al Omari Moahmmed Ahmed
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These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions
Procedia PDF Downloads 4508504 The Impact of Artificial Intelligence on Human Rights Development
Authors: Romany Wagih Farag Zaky
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The relationship between development and human rights has long been the subject of academic debate. To understand the dynamics between these two concepts, various principles are adopted, from the right to development to development-based human rights. Despite the initiatives taken, the relationship between development and human rights remains unclear. However, the overlap between these two views and the idea that efforts should be made in the field of human rights have increased in recent years. It is then evaluated whether the right to sustainable development is acceptable or not. The article concludes that the principles of sustainable development are directly or indirectly recognized in various human rights instruments, which is a good answer to the question posed above. This book therefore cites regional and international human rights agreements such as , as well as the jurisprudence and interpretative guidelines of human rights institutions, to prove this hypothesis.Keywords: sustainable development, human rights, the right to development, the human rights-based approach to development, environmental rights, economic development, social sustainability human rights protection, human rights violations, workers’ rights, justice, security
Procedia PDF Downloads 218503 A Tool Tuning Approximation Method: Exploration of the System Dynamics and Its Impact on Milling Stability When Amending Tool Stickout
Authors: Nikolai Bertelsen, Robert A. Alphinas, Klaus B. Orskov
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The shortest possible tool stickout has been the traditional go-to approach with expectations of increased stability and productivity. However, experimental studies at Danish Advanced Manufacturing Research Center (DAMRC) have proven that for some tool stickout lengths, there exist local productivity optimums when utilizing the Stability Lobe Diagrams for chatter avoidance. This contradicts with traditional logic and the best practices taught to machinists. This paper explores the vibrational characteristics and behaviour of a milling system over the tool stickout length. The experimental investigation has been conducted by tap testing multiple endmills where the tool stickout length has been varied. For each length, the modal parameters have been recorded and mapped to visualize behavioural tendencies. Furthermore, the paper explores the correlation between the modal parameters and the Stability Lobe Diagram to outline the influence and importance of each parameter in a multi-mode system. The insights are conceptualized into a tool tuning approximation solution. It builds on an almost linear change in the natural frequencies when amending tool stickout, which results in changed positions of the Chatter-free Stability Lobes. Furthermore, if the natural frequency of two modes become too close, it will onset of the dynamic absorber effect phenomenon. This phenomenon increases the critical stable depth of cut, allowing for a more stable milling process. Validation tests on the tool tuning approximation solution have shown varying success of the solution. This outlines the need for further research on the boundary conditions of the solution to understand at which conditions the tool tuning approximation solution is applicable. If the conditions get defined, the conceptualized tool tuning approximation solution outlines an approach for quick and roughly approximating tool stickouts with the potential for increased stiffness and optimized productivity.Keywords: milling, modal parameters, stability lobes, tap testing, tool tuning
Procedia PDF Downloads 1138502 On the Inequality between Queue Length and Virtual Waiting Time in Open Queueing Networks under Conditions of Heavy Traffic
Authors: Saulius Minkevicius, Edvinas Greicius
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The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the inequality in an open queueing network and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of customers in an open queueing network.Keywords: fluid approximation, heavy traffic, models of information systems, open queueing network, queue length of customers, queueing theory
Procedia PDF Downloads 2598501 A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement
Authors: Tudor Barbu
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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes
Procedia PDF Downloads 2858500 An 8-Bit, 100-MSPS Fully Dynamic SAR ADC for Ultra-High Speed Image Sensor
Authors: F. Rarbi, D. Dzahini, W. Uhring
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In this paper, a dynamic and power efficient 8-bit and 100-MSPS Successive Approximation Register (SAR) Analog-to-Digital Converter (ADC) is presented. The circuit uses a non-differential capacitive Digital-to-Analog (DAC) architecture segmented by 2. The prototype is produced in a commercial 65-nm 1P7M CMOS technology with 1.2-V supply voltage. The size of the core ADC is 208.6 x 103.6 µm2. The post-layout noise simulation results feature a SNR of 46.9 dB at Nyquist frequency, which means an effective number of bit (ENOB) of 7.5-b. The total power consumption of this SAR ADC is only 1.55 mW at 100-MSPS. It achieves then a figure of merit of 85.6 fJ/step.Keywords: CMOS analog to digital converter, dynamic comparator, image sensor application, successive approximation register
Procedia PDF Downloads 3918499 Least Squares Solution for Linear Quadratic Gaussian Problem with Stochastic Approximation Approach
Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo
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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation
Procedia PDF Downloads 1428498 Mean-Field Type Modeling of Non-Local Congestion in Pedestrian Crowd Dynamics
Authors: Alexander Aurell
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One of the latest trends in the modeling of human crowds is the mean-field game approach. In the mean-field game approach, the motion of a human crowd is described by a nonstandard stochastic optimal control problem. It is nonstandard since congestion is considered, introduced through a dependence in the performance functional on the distribution of the crowd. This study extends the class of mean-field pedestrian crowd models to allow for non-local congestion and arbitrary, but finitely, many interacting crowds. The new congestion feature grants pedestrians a 'personal space' where crowding is undesirable. The model is treated as a mean-field type game which is derived from a particle picture. This, in contrast to a mean-field game, better describes a situation where the crowd can be controlled by a central planner. The latter is suitable for decentralized situations. Solutions to the mean-field type game are characterized via a Pontryagin-type Maximum Principle.Keywords: congestion, crowd dynamics, interacting populations, mean-field approximation, optimal control
Procedia PDF Downloads 412