Search results for: Radial basis function network

Authors: Brenden M. Shutt, Lubjana Beshaj, Paul L. Goethals, Ambrose Kam

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Communication security is of particular interest to military data networks. A relatively novel approach to network security is blockchain, a cryptographically secured distribution ledger with a decentralized consensus mechanism for data transaction processing. Recent advances in blockchain technology have proposed new techniques for both data validation and trust management, as well as different frameworks for managing dataflow. The purpose of this work is to test the feasibility of different blockchain architectures as applied to military command and control networks. Various architectures are tested through discrete-event simulation and the feasibility is determined based upon a blockchain design’s ability to maintain long-term stable performance at industry standards of throughput, network latency, and security. This work proposes a consortium blockchain architecture with a computationally inexpensive consensus mechanism, one that leverages a Proof-of-Identity (PoI) concept and a reputation management mechanism.

Keywords: Blockchain, command & control network, discrete-event simulation, reputation management.

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Authors: G. C. Mahata, A. Goswami

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This paper deals with infinite time horizon fuzzy Economic Order Quantity (EOQ) models for deteriorating items with  stock dependent demand rate and nonlinear holding costs by taking deterioration rate θ0 as a triangular fuzzy number  (θ0 −δ 1, θ0, θ0 +δ 2), where 1 2 0 0 <δ ,δ <θ are fixed real numbers. The traditional parameters such as unit cost and ordering  cost have been kept constant but holding cost is considered to vary. Two possibilities of variations in the holding cost function namely, a non-linear function of the length of time for which the item is held in stock and a non-linear function of the amount of on-hand inventory have been used in the models. The approximate optimal solution for the fuzzy cost functions in both these cases have been obtained and the effect of non-linearity in holding costs is studied with the help of a numerical example.

Keywords: Inventory Model, Deterioration, Holding Cost, Fuzzy Total Cost, Extension Principle.

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Authors: Ajoy Kumar Das, Prasenjit Dey

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Heat transfer due to forced convection of copper water based nanofluid has been predicted by Artificial Neural network (ANN). The present nanofluid is formed by mixing copper nanoparticles in water and the volume fractions are considered here are 0% to 15% and the Reynolds number are kept constant at 100. The back propagation algorithm is used to train the network. The present ANN is trained by the input and output data which has been obtained from the numerical simulation, performed in finite volume based Computational Fluid Dynamics (CFD) commercial software Ansys Fluent. The numerical simulation based results are compared with the back propagation based ANN results. It is found that the forced convection heat transfer of water based nanofluid can be predicted correctly by ANN. It is also observed that the back propagation ANN can predict the heat transfer characteristics of nanofluid very quickly compared to standard CFD method.

Keywords: Forced convection, Square cylinder, nanofluid, neural network.

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Authors: Hakim S. Sultan Aljibori

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Effect of geometry on crushing behavior, energy absorption and failure mode of woven roving jute fiber/epoxy laminated composite tubes were experimentally studied. Investigations were carried out on three different geometrical types of composite tubes (circular, square and radial corrugated) subjected to axial compressive loading. It was observed in axial crushing study that the load bearing capability is significantly influenced by corrugation geometry. The influence of geometries of specimens was supported by the plotted load – displacement curves of the tests.

Keywords: Crushing behavior, jute fiber, composite tubes andSpecific energy absorption

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Authors: Seyed Hossein Iranmanesh, Mansoureh Zarezadeh

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This paper presents an application of Artificial Neural Network (ANN) to forecast actual cost of a project based on the earned value management system (EVMS). For this purpose, some projects randomly selected based on the standard data set , and it is produced necessary progress data such as actual cost ,actual percent complete , baseline cost and percent complete for five periods of project. Then an ANN with five inputs and five outputs and one hidden layer is trained to produce forecasted actual costs. The comparison between real and forecasted data show better performance based on the Mean Absolute Percentage Error (MAPE) criterion. This approach could be applicable to better forecasting the project cost and result in decreasing the risk of project cost overrun, and therefore it is beneficial for planning preventive actions.

Keywords: Earned Value Management System (EVMS), Artificial Neural Network (ANN), Estimate At Completion, Forecasting Methods, Project Performance Measurement.

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Authors: Zhizhong Jiang, Peter Naudé, Binghua Jiang

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Effective evaluation of software development effort is an important issue during project plan. This study provides a model to predict development effort based on the software size estimated with function points. We generalize the average amount of effort spent on each phase of the development, and give the estimates for the effort used in software building, testing, and implementation. Finally, this paper finds a strong correlation between software defects and software size. As the size of software constantly increases, the quality remains to be a matter which requires major concern.

Keywords: Development effort, function points, software quality, software size.

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Authors: Mehdi Seifbarghy, Keyvan Roshan

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Main goal of preventive healthcare problems are at decreasing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The levels of establishment and staffing costs along with summation of the travel and waiting time that clients spent are considered as objectives functions of the proposed nonlinear integer programming model. In this paper, we have proposed a bi-objective mathematical model for designing a network of preventive healthcare facilities so as to minimize aforementioned objectives, simultaneously. Moreover, each facility acts as M/M/1 queuing system. The number of facilities to be established, the location of each facility, and the level of technology for each facility to be chosen are provided as the main determinants of a healthcare facility network. Finally, to demonstrate performance of the proposed model, four multi-objective decision making techniques are presented to solve the model.

Keywords: Preventive healthcare problems, Non-linear integer programming models, Multi-objective decision making techniques

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Authors: Marios N. Moschakis

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The increasing penetration of Distributed Generation and storage connected to the distribution network via PWM converters increases the possibility of a DC-component (offset) in voltage or current flowing into the grid. This occurs when even harmonics are present in the network voltage. DC-components can affect the operation and safety of several grid components. Therefore, an investigation of the way they are produced is important in order to take appropriate measures for their elimination. Further research on DC-components that appear on output voltage of converters is performed for different parameters of PWM technique and characteristics of even harmonics.

Keywords: Asymmetric even harmonics, DC-offsets, distributed generation, electric machine drive systems, power quality.

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Authors: K. Jayakumar, S. Thangavel

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In this paper proposed the effective fault detection of industrial drives by using Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate, and execution time.

Keywords: Biorthogonal Wavelet Transform, Posterior Probabilistic Neural Network, Induction Motor.

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Authors: Zeynep İltüzer Samur, Gül Tekin Temur

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Due to the increasing and varying risks that economic units face with, derivative instruments gain substantial importance, and trading volumes of derivatives have reached very significant level. Parallel with these high trading volumes, researchers have developed many different models. Some are parametric, some are nonparametric. In this study, the aim is to analyse the success of artificial neural network in pricing of options with S&P 100 index options data. Generally, the previous studies cover the data of European type call options. This study includes not only European call option but also American call and put options and European put options. Three data sets are used to perform three different ANN models. One only includes data that are directly observed from the economic environment, i.e. strike price, spot price, interest rate, maturity, type of the contract. The others include an extra input that is not an observable data but a parameter, i.e. volatility. With these detail data, the performance of ANN in put/call dimension, American/European dimension, moneyness dimension is analyzed and whether the contribution of the volatility in neural network analysis make improvement in prediction performance or not is examined. The most striking results revealed by the study is that ANN shows better performance when pricing call options compared to put options; and the use of volatility parameter as an input does not improve the performance.

Keywords: Option Pricing, Neural Network, S&P 100 Index, American/European options

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Authors: Taneli Eisto, Venlakaisa Hölttä, Katrine Mahlamäki, Janne Kollanus, Marko Nieminen

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Early supplier involvement (ESI) benefits new product development projects several ways. Nevertheless, many castuser companies do not know the advantages of ESI and therefore do not utilize it. This paper presents reasons why to utilize ESI in casting industry and how that can be done. Further, this paper presents advantages and challenges related to ESI in casting industry, and introduces a Casting-Network Collaboration Model. The model presents practices for companies to build advantageous collaborative relationships. More detailed, the model describes three levels for company-network relationships in casting industry with different degrees of collaboration, and requirements for operating in each level. In our research, ESI was found to influence, for example, on project time, component cost, and quality. In addition, challenges related to ESI, such as, a lack of mutual trust and unawareness about the advantages were found. Our research approach was a case study including four cases.

Keywords: Casting Industry, Collaboration Model, EarlySupplier Involvement, New Product Development.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

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This paper proposes an efficient method for the design of two channel quadrature mirror filter (QMF) bank. To achieve minimum value of reconstruction error near to perfect reconstruction, a linear optimization process has been proposed. Prototype low pass filter has been designed using Kaiser window function. The modified algorithm has been developed to optimize the reconstruction error using linear objective function through iteration method. The result obtained, show that the performance of the proposed algorithm is better than that of the already exists methods.

Keywords: Filterbank, near perfect reconstruction, Kaiserwindow, QMF.

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Authors: Noman Khan, B. S. Chowdhry, A.Q.K Rajput

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Integrated fiber-wireless (FiWi) access networks are a viable solution that can deliver the high profile quadruple play services. Passive optical networks (PON) networks integrated with wireless access networks provide ubiquitous characteristics for high bandwidth applications. Operation of PON improves by employing a variety of multiplexing techniques. One of it is time division/wavelength division multiplexed (TDM/WDM) architecture that improves the performance of optical-wireless access networks. This paper proposes a novel feedback-based TDM/WDM-PON architecture and introduces a model of integrated PON-FiWi networks. Feedback-based link architecture is an efficient solution to improves the performance of optical-line-terminal (OLT) and interlink optical-network-units (ONUs) communication. Furthermore, the feedback-based WDM/TDM-PON architecture is compared with existing architectures in terms of capacity of network throughput.

Keywords: Fiber-wireless (FiWi), Passive Optical Network (PON), TDM/WDM architecture

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Authors: S. Akhila, M. Lakshminarayana

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In cellular networks, limited availability of resources has to be tapped to its fullest potential. In view of this aspect, a sophisticated averaging and voting technique has been discussed in this paper, wherein the radio resources available are utilized to the fullest value by taking into consideration, several network and radio parameters which decide on when the handover has to be made and thereby reducing the load on Base station .The increase in the load on the Base station might be due to several unnecessary handover taking place which can be eliminated by making judicious use of the radio and network parameters.

Keywords: Averaging and Voting, Handover, QoS.

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Authors: Piyangkun Kukutapan, Siridech Boonsang

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The article proposes maximum power point tracking without mechanical sensor using Multilayer Perceptron Neural Network (MLPNN). The aim of article is to reduce the cost and complexity but still retain efficiency. The experimental is that duty cycle is generated maximum power, if it has suitable qualification. The measured data from DC generator, voltage (V), current (I), power (P), turnover rate of power (dP), and turnover rate of voltage (dV) are used as input for MLPNN model. The output of this model is duty cycle for driving the converter. The experiment implemented using Arduino Uno board. This diagram is compared to MPPT using MLPNN and P&O control (Perturbation and Observation control). The experimental results show that the proposed MLPNN based approach is more efficiency than P&O algorithm for this application.

Keywords: Maximum power point tracking, multilayer perceptron neural network, optimal duty cycle.

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Authors: Feng Xiao, Zhou Hongyu, YuCaixia

Abstract:

Based on an analysis of the current research and application of Road maintenance, geographic information system (WebGIS) and ArcGIS Server, the platform overhead construction for Road maintenance development is studied and the key issues are presented, including the organization and design of spatial data on the basis of the geodatabase technology, middleware technology, tiles cache index technology and dynamic segmentation of WebGIS. Road maintenance geographic information platform is put forward through the researching ideas of analysis of the system design. The design and application of WebGIS system are discussed on the basis of a case study of BaNan district of Chongqing highway maintenance management .The feasibility of the theories and methods are validated through the system.

Keywords: WebGIS, Tile, Road maintenance, dynamic segmentation

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Authors: Mohammad Heidari

Abstract:

Horizontal wells are proven to be better producers because they can be extended for a long distance in the pay zone. Engineers have the technical means to forecast the well productivity for a given horizontal length. However, experiences have shown that the actual production rate is often significantly less than that of forecasted. It is a difficult task, if not impossible to identify the real reason why a horizontal well is not producing what was forecasted. Often the source of problem lies in the drilling of horizontal section such as permeability reduction in the pay zone due to mud invasion or snaky well patterns created during drilling. Although drillers aim to drill a constant inclination hole in the pay zone, the more frequent outcome is a sinusoidal wellbore trajectory. The two factors, which play an important role in wellbore tortuosity, are the inclination and side force at bit. A constant inclination horizontal well can only be drilled if the bit face is maintained perpendicular to longitudinal axis of bottom hole assembly (BHA) while keeping the side force nil at the bit. This approach assumes that there exists no formation force at bit. Hence, an appropriate BHA can be designed if bit side force and bit tilt are determined accurately. The Artificial Neural Network (ANN) is superior to existing analytical techniques. In this study, the neural networks have been employed as a general approximation tool for estimation of the bit side forces. A number of samples are analyzed with ANN for parameters of bit side force and the results are compared with exact analysis. Back Propagation Neural network (BPN) is used to approximation of bit side forces. Resultant low relative error value of the test indicates the usability of the BPN in this area.

Keywords: Artificial Neural Network, BHA, Horizontal Well, Stabilizer.

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Authors: Pedram Behyar, Maryam Heidari, Zahra Bayat

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the purpose of this research is to identify and clarify factors which have positive effect among user satisfaction and their social networking through websites. The examined factors in this research are; innovation, ease of use, trustworthy and customer support which are defined as satisfaction factors. To obtain reliable research approaches and to have better result in this research four hypothesizes used to test. This hypothesis testing has been done by correlation, regression and test of normality by using “SPSS16" also the data which was analyzed by this software. this data was gathered from prepaid questionnaire.

Keywords: Customer Satisfaction, Social Network Website

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Authors: Boregowda S.B., Hemanth Kumar A.R. Babu N.V, Puttamadappa C., And H.S Mruthyunjaya

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In the past few years, the use of wireless sensor networks (WSNs) potentially increased in applications such as intrusion detection, forest fire detection, disaster management and battle field. Sensor nodes are generally battery operated low cost devices. The key challenge in the design and operation of WSNs is to prolong the network life time by reducing the energy consumption among sensor nodes. Node clustering is one of the most promising techniques for energy conservation. This paper presents a novel clustering algorithm which maximizes the network lifetime by reducing the number of communication among sensor nodes. This approach also includes new distributed cluster formation technique that enables self-organization of large number of nodes, algorithm for maintaining constant number of clusters by prior selection of cluster head and rotating the role of cluster head to evenly distribute the energy load among all sensor nodes.

Keywords: Clustering algorithms, Cluster head, Energy consumption, Sensor nodes, and Wireless sensor networks.

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Authors: E. F. P. Leme, L. J. R. Lopez, D. G. Goroso

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In this paper as showed a non-invasive 3D eye tracker for optometry clinical applications. Measurements of biomechanical variables in clinical practice have many font of errors associated with traditional procedments such cover test (CT), near point of accommodation (NPC), eye ductions (ED), eye vergences (EG) and, eye versions (ES). Ocular motility should always be tested but all evaluations have a subjective interpretations by practitioners, the results is based in clinical experiences, repeatability and accuracy don-t exist. Optometric-lab is a tool with 3 (tree) analogical video cameras triggered and synchronized in one acquisition board AD. The variables globe rotation angle and velocity can be quantified. Data record frequency was performed with 27Hz, camera calibration was performed in a know volume and image radial distortion adjustments.

Keywords: Eye Tracking, strabismus, eye movements, optometry.

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Authors: Faizal A. Samman, Thomas Hollstein, Manfred Glesner

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This paper presents design trade-off and performance impacts of the amount of pipeline phase of control path signals in a wormhole-switched network-on-chip (NoC). The numbers of the pipeline phase of the control path vary between two- and one-cycle pipeline phase. The control paths consist of the routing request paths for output selection and the arbitration paths for input selection. Data communications between on-chip routers are implemented synchronously and for quality of service, the inter-router data transports are controlled by using a link-level congestion control to avoid lose of data because of an overflow. The trade-off between the area (logic cell area) and the performance (bandwidth gain) of two proposed NoC router microarchitectures are presented in this paper. The performance evaluation is made by using a traffic scenario with different number of workloads under 2D mesh NoC topology using a static routing algorithm. By using a 130-nm CMOS standard-cell technology, our NoC routers can be clocked at 1 GHz, resulting in a high speed network link and high router bandwidth capacity of about 320 Gbit/s. Based on our experiments, the amount of control path pipeline stages gives more significant impact on the NoC performance than the impact on the logic area of the NoC router.

Keywords: Network-on-Chip, Synchronous Parallel Pipeline, Router Architecture, Wormhole Switching

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Authors: Mario Mastriani, Marcelo Naiouf

Abstract:

This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.

Keywords: Quantum Algebra, correlation matrix memory, Dirac notation, orthogonalisation.

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Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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Authors: Mohamed K. Watfa, Khaled Abdel Naby, Chetan Govind Bhatia

Abstract:

With the exponential rise in the number of multimedia applications available, the best-effort service provided by the Internet today is insufficient. Researchers have been working on new architectures like the Next Generation Network (NGN) which, by definition, will ensure Quality of Service (QoS) in an all-IP based network [1]. For this approach to become a reality, reservation of bandwidth is required per application per user. WiMAX (Worldwide Interoperability for Microwave Access) is a wireless communication technology which has predefined levels of QoS which can be provided to the user [4]. IPv6 has been created as the successor for IPv4 and resolves issues like the availability of IP addresses and QoS. This paper provides a design to use the power of WiMAX as an NSP (Network Service Provider) for NGN using IPv6. The use of the Traffic Class (TC) field and the Flow Label (FL) field of IPv6 has been explained for making QoS requests and grants [6], [7]. Using these fields, the processing time is reduced and routing is simplified. Also, we define the functioning of the ASN gateway and the NGN gateway (NGNG) which are edge node interfaces in the NGNWiMAX design. These gateways ensure QoS management through built in functions and by certain physical resources and networking capabilities.

Keywords: WiMAX, NGN, QoS, IPv6, Flow Label, ASNGateway

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Authors: S.Ponmalar, S.Sundaravadivelu

Abstract:

Traditional optical networks are gradually evolving towards intelligent optical networks due to the need for faster bandwidth provisioning, protection and restoration of the network that can be accomplished with devices like optical switch, add drop multiplexer and cross connects. Since dense wavelength multiplexing forms the physical layer for intelligent optical networking, the roll of high speed all optical switch is important. This paper analyzes such an ultra-high speed polymer electro-optic switch. The performances of the 2x2 optical waveguide switch with rectangular, triangular and trapezoidal grating profiles on various device parameters are analyzed. The simulation result shows that trapezoidal grating is the optimized structure which has the coupling length of 81μm and switching voltage of 11V for the operating wavelength of 1550nm. The switching time for this proposed switch is 0.47 picosecond. This makes the proposed switch to be an important element in the intelligent optical network.

Keywords: Intelligent optical network, optical switch, electrooptic effect, coupled mode theory, waveguide grating structures

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Authors: S. Beyou, B. Grondin-Perez, M. Benne, C. Damour, J.-P. Chabriat

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The industrial process of the sugar cane crystallization produces a residual that still contains a lot of soluble sucrose and the objective of the factory is to improve its extraction. Therefore, there are substantial losses justifying the search for the optimization of the process. Crystallization process studied on the industrial site is based on the “three massecuites process". The third step of this process constitutes the final stage of exhaustion of the sucrose dissolved in the mother liquor. During the process of the third step of crystallization (Ccrystallization), the phase that is studied and whose control is to be improved, is the growing phase (crystal growth phase). The study of this process on the industrial site is a problem in its own. A control scheme is proposed to improve the standard PID control law used in the factory. An auto-tuning PID controller based on instantaneous linearization of a neural network is then proposed.

Keywords: Auto-tuning, PID, Instantaneous linearization, Neural network, Non linear process, C-crystallisation.

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Authors: A. Allirani, M. Suganthi

Abstract:

Data gathering is an essential operation in wireless sensor network applications. So it requires energy efficiency techniques to increase the lifetime of the network. Similarly, clustering is also an effective technique to improve the energy efficiency and network lifetime of wireless sensor networks. In this paper, an energy efficient cluster formation protocol is proposed with the objective of achieving low energy dissipation and latency without sacrificing application specific quality. The objective is achieved by applying randomized, adaptive, self-configuring cluster formation and localized control for data transfers. It involves application - specific data processing, such as data aggregation or compression. The cluster formation algorithm allows each node to make independent decisions, so as to generate good clusters as the end. Simulation results show that the proposed protocol utilizes minimum energy and latency for cluster formation, there by reducing the overhead of the protocol.

Keywords: Sensor networks, Low latency, Energy sorting protocol, data processing, Cluster formation.

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Authors: Guang Sun, Yong Li, Yuanyuan Zhang, Shijun Lin, Li Su, Depeng Jin, Lieguang zeng

Abstract:

Network on Chip (NoC) has emerged as a promising on chip communication infrastructure. Three Dimensional Integrate Circuit (3D IC) provides small interconnection length between layers and the interconnect scalability in the third dimension, which can further improve the performance of NoC. Therefore, in this paper, a hierarchical cluster-based interconnect architecture is merged with the 3D IC. This interconnect architecture significantly reduces the number of long wires. Since this architecture only has approximately a quarter of routers in 3D mesh-based architecture, the average number of hops is smaller, which leads to lower latency and higher throughput. Moreover, smaller number of routers decreases the area overhead. Meanwhile, some dual links are inserted into the bottlenecks of communication to improve the performance of NoC. Simulation results demonstrate our theoretical analysis and show the advantages of our proposed architecture in latency, throughput and area, when compared with 3D mesh-based architecture.

Keywords: Network on Chip (NoC), interconnect architecture, performance, area, Three Dimensional Integrate Circuit (3D IC).

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper deals with the project selection problem. Project selection problem is one of the problems arose firstly in the field of operations research following some production concepts from primary product mix problem. Afterward, introduction of managerial considerations into the project selection problem have emerged qualitative factors and criteria to be regarded as well as quantitative ones. To overcome both kinds of criteria, an analytic network process is developed in this paper enhanced with fuzzy sets theory to tackle the vagueness of experts- comments to evaluate the alternatives. Additionally, a modified version of Least-Square method through a non-linear programming model is augmented to the developed group decision making structure in order to elicit the final weights from comparison matrices. Finally, a case study is considered by which developed structure in this paper is validated. Moreover, a sensitivity analysis is performed to validate the response of the model with respect to the condition alteration.

Keywords: Analytic network process, Fuzzy sets theory, Nonlinear programming, Project selection.

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Authors: Peter Benneth, Tsaroh N. Theophilus, Prince Benjamin

Abstract:

This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.

Keywords: Legendre transformation method, Optimal investment strategy, Ito’s lemma, Hamilton Jacobi Bellman equation, Geometric Brownian motion, financial market.

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