Search results for: Neural function.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3166

Search results for: Neural function.

1336 Selection Initial modes for Belief K-modes Method

Authors: Sarra Ben Hariz, Zied Elouedi, Khaled Mellouli

Abstract:

The belief K-modes method (BKM) approach is a new clustering technique handling uncertainty in the attribute values of objects in both the cluster construction task and the classification one. Like the standard version of this method, the BKM results depend on the chosen initial modes. So, one selection method of initial modes is developed, in this paper, aiming at improving the performances of the BKM approach. Experiments with several sets of real data show that by considered the developed selection initial modes method, the clustering algorithm produces more accurate results.

Keywords: Clustering, Uncertainty, Belief function theory, Belief K-modes Method, Initial modes selection.

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1335 Hybrid Modeling and Optimal Control of a Two-Tank System as a Switched System

Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

In the past decade, because of wide applications of hybrid systems, many researchers have considered modeling and control of these systems. Since switching systems constitute an important class of hybrid systems, in this paper a method for optimal control of linear switching systems is described. The method is also applied on the two-tank system which is a much appropriate system to analyze different modeling and control techniques of hybrid systems. Simulation results show that, in this method, the goals of control and also problem constraints can be satisfied by an appropriate selection of cost function.

Keywords: Hybrid systems, optimal control, switched systems, two-tank system

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1334 An Accurate Method for Phylogeny Tree Reconstruction Based on a Modified Wild Dog Algorithm

Authors: Essam Al Daoud

Abstract:

This study solves a phylogeny problem by using modified wild dog pack optimization. The least squares error is considered as a cost function that needs to be minimized. Therefore, in each iteration, new distance matrices based on the constructed trees are calculated and used to select the alpha dog. To test the suggested algorithm, ten homologous genes are selected and collected from National Center for Biotechnology Information (NCBI) databanks (i.e., 16S, 18S, 28S, Cox 1, ITS1, ITS2, ETS, ATPB, Hsp90, and STN). The data are divided into three categories: 50 taxa, 100 taxa and 500 taxa. The empirical results show that the proposed algorithm is more reliable and accurate than other implemented methods.

Keywords: Least squares, neighbor joining, phylogenetic tree, wild dogpack.

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1333 Adaptive Neuro-Fuzzy Inference System for Financial Trading using Intraday Seasonality Observation Model

Authors: A. Kablan

Abstract:

The prediction of financial time series is a very complicated process. If the efficient market hypothesis holds, then the predictability of most financial time series would be a rather controversial issue, due to the fact that the current price contains already all available information in the market. This paper extends the Adaptive Neuro Fuzzy Inference System for High Frequency Trading which is an expert system that is capable of using fuzzy reasoning combined with the pattern recognition capability of neural networks to be used in financial forecasting and trading in high frequency. However, in order to eliminate unnecessary input in the training phase a new event based volatility model was proposed. Taking volatility and the scaling laws of financial time series into consideration has brought about the development of the Intraday Seasonality Observation Model. This new model allows the observation of specific events and seasonalities in data and subsequently removes any unnecessary data. This new event based volatility model provides the ANFIS system with more accurate input and has increased the overall performance of the system.

Keywords: Adaptive Neuro-fuzzy Inference system, High Frequency Trading, Intraday Seasonality Observation Model.

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1332 Vibration Base Identification of Impact Force Using Genetic Algorithm

Authors: R. Hashemi, M.H.Kargarnovin

Abstract:

This paper presents the identification of the impact force acting on a simply supported beam. The force identification is an inverse problem in which the measured response of the structure is used to determine the applied force. The identification problem is formulated as an optimization problem and the genetic algorithm is utilized to solve the optimization problem. The objective function is calculated on the difference between analytical and measured responses and the decision variables are the location and magnitude of the applied force. The results from simulation show the effectiveness of the approach and its robustness vs. the measurement noise and sensor location.

Keywords: Genetic Algorithm, Inverse problem, Optimization, Vibration.

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1331 Exergetic Comparison between Three Configurations of Two Stage Vapor Compression Refrigeration Systems

Authors: Wafa Halfaoui Mbarek, Khir Tahar, Ben Brahim Ammar

Abstract:

This study reports a comparison from an exergetic point of view between three configurations of vapor compression industrial refrigeration systems operating with R134a as working fluid. The performances of the different cycles are analyzed as function of several operating parameters such as condensing temperature and inter stage pressure. In addition, the contributions of component exergy destruction to the total exergy destruction are obtained for each system. The results are estimated to be used in the selection of the most advantageous configuration from an exergetic view point.

Keywords: Vapor compression, exergy, destruction, efficiency, R134a.

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1330 A Web Service Platform for Support Multiple Programming Language to Access Biomedical Image Databases

Authors: Mohd Kamir Yusof, Suhailan Dato' Safei

Abstract:

Images are important in disease research, education, and clinical medicine. This paper presents a Web Service Platform (WSP) for support multiple programming languages to access image from biomedical databases. The main function WSP is to allow web users access image from biomedical databases. The WSP will receive web user-s queries. After that, it will send to Querying Server (QS) and the QS will search and retrieve data from biomedical databases. Finally, the information will display to the web users. Simple application is developed and tested for experiment purpose. Result from experiment indicated WSP can be used in biomedical environment.

Keywords: Biomedical, Image, Web Service Platform

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1329 Optimization of a Triangular Fin with Variable Fin Base Thickness

Authors: Hyung Suk Kang

Abstract:

A triangular fin with variable fin base thickness is analyzed and optimized using a two-dimensional analytical method. The influence of fin base height and fin base thickness on the temperature in the fin is listed. For the fixed fin volumes, the maximum heat loss, the corresponding optimum fin effectiveness, fin base height and fin tip length as a function of the fin base thickness, convection characteristic number and dimensionless fin volume are represented. One of the results shows that the optimum heat loss increases whereas the corresponding optimum fin effectiveness decreases with the increase of fin volume.

Keywords: A triangular fin, Convection characteristic number, Heat loss, Fin base thickness.

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1328 A Decision Support System Based on Leprosy Scales

Authors: Dennys Robson Girardi, Hugo Bulegon, Claudia Maria Moro Barra

Abstract:

Leprosy is an infectious disease caused by Mycobacterium Leprae, this disease, generally, compromises the neural fibers, leading to the development of disability. Disabilities are changes that limit daily activities or social life of a normal individual. When comes to leprosy, the study of disability considered the functional limitation (physical disabilities), the limitation of activity and social participation, which are measured respectively by the scales: EHF, SALSA and PARTICIPATION SCALE. The objective of this work is to propose an on-line monitoring of leprosy patients, which is based on information scales EHF, SALSA and PARTICIPATION SCALE. It is expected that the proposed system is applied in monitoring the patient during treatment and after healing therapy of the disease. The correlations that the system is between the scales create a variety of information, presented the state of the patient and full of changes or reductions in disability. The system provides reports with information from each of the scales and the relationships that exist between them. This way, health professionals, with access to patient information, can intervene with techniques for the Prevention of Disability. Through the automated scale, the system shows the level of the patient and allows the patient, or the responsible, to take a preventive measure. With an online system, it is possible take the assessments and monitor patients from anywhere.

Keywords: Leprosy, Medical Informatics, Decision SupportSystem, Disability.

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1327 Enhanced Clustering Analysis and Visualization Using Kohonen's Self-Organizing Feature Map Networks

Authors: Kasthurirangan Gopalakrishnan, Siddhartha Khaitan, Anshu Manik

Abstract:

Cluster analysis is the name given to a diverse collection of techniques that can be used to classify objects (e.g. individuals, quadrats, species etc). While Kohonen's Self-Organizing Feature Map (SOFM) or Self-Organizing Map (SOM) networks have been successfully applied as a classification tool to various problem domains, including speech recognition, image data compression, image or character recognition, robot control and medical diagnosis, its potential as a robust substitute for clustering analysis remains relatively unresearched. SOM networks combine competitive learning with dimensionality reduction by smoothing the clusters with respect to an a priori grid and provide a powerful tool for data visualization. In this paper, SOM is used for creating a toroidal mapping of two-dimensional lattice to perform cluster analysis on results of a chemical analysis of wines produced in the same region in Italy but derived from three different cultivators, referred to as the “wine recognition data" located in the University of California-Irvine database. The results are encouraging and it is believed that SOM would make an appealing and powerful decision-support system tool for clustering tasks and for data visualization.

Keywords: Artificial neural networks, cluster analysis, Kohonen maps, wine recognition.

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1326 Simplex Method for Fuzzy Variable Linear Programming Problems

Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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1325 Texture Observation of Bending by XRD and EBSD Method

Authors: Takashi Sakai, Yuri Shimomura

Abstract:

The crystal orientation is a factor that affects the microscopic material properties. Crystal orientation determines the anisotropy of the polycrystalline material. And it is closely related to the mechanical properties of the material. In this paper, for pure copper polycrystalline material, two different methods; X-Ray Diffraction (XRD) and Electron Backscatter Diffraction (EBSD); and the crystal orientation were analyzed. In the latter method, it is possible that the X-ray beam diameter is thicker as compared to the former, to measure the crystal orientation macroscopically relatively. By measurement of the above, we investigated the change in crystal orientation and internal tissues of pure copper.

Keywords: Bending, electron backscatter diffraction, X-ray diffraction, microstructure, IPF map, orientation distribution function.

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1324 Improved Robust Stability and Stabilization Conditions of Discrete-time Delayed System

Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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1323 Supply Air Pressure Control of HVAC System Using MPC Controller

Authors: P. Javid, A. Aeenmehr, J. Taghavifar

Abstract:

In this paper, supply air pressure of HVAC system has been modeled with second-order transfer function plus dead-time. In HVAC system, the desired input has step changes, and the output of proposed control system should be able to follow the input reference, so the idea of using model based predictive control is proceeded and designed in this paper. The closed loop control system is implemented in MATLAB software and the simulation results are provided. The simulation results show that the model based predictive control is able to control the plant properly.

Keywords: Air conditioning system, GPC, dead time, Air supply control.

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1322 Bifurcation and Chaos of the Memristor Circuit

Authors: Wang Zhulin, Min Fuhong, Peng Guangya, Wang Yaoda, Cao Yi

Abstract:

In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.

Keywords: Memristor, chaotic circuit, dynamical behavior, chaotic system.

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1321 Fixture Layout Optimization for Large Metal Sheets Using Genetic Algorithm

Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The geometric errors in the manufacturing process can be reduced by optimal positioning of the fixture elements in the fixture to make the workpiece stiff. We propose a new fixture layout optimization method N-3-2-1 for large metal sheets in this paper that combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of the nodal deflection normal to the surface of the workpiece. Two different kinds of case studies are presented, and optimal position of the fixturing element is obtained for different cases.

Keywords: Fixture layout, optimization, fixturing element, genetic algorithm.

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1320 Stimulus-Dependent Polyrhythms of Central Pattern Generator Hardware

Authors: Le Zhao, Alain Nogaret

Abstract:

We have built universal central pattern generator (CPG) hardware by interconnecting Hodgkin-Huxley neurons with reciprocally inhibitory synapses. We investigate the dynamics of neuron oscillations as a function of the time delay between current steps applied to individual neurons. We demonstrate stimulus dependent switching between spiking polyrhythms and map the phase portraits of the neuron oscillations to reveal the basins of attraction of the system. We experimentally study the dependence of the attraction basins on the network parameters: The neuron response time and the strength of inhibitory connections.

Keywords: Central pattern generator, winnerless competition principle.

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1319 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers

Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

Abstract:

In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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1318 Analysis of Event-related Response in Human Visual Cortex with fMRI

Authors: Ayesha Zaman, Tanvir Atahary, Shahida Rafiq

Abstract:

Functional Magnetic Resonance Imaging(fMRI) is a noninvasive imaging technique that measures the hemodynamic response related to neural activity in the human brain. Event-related functional magnetic resonance imaging (efMRI) is a form of functional Magnetic Resonance Imaging (fMRI) in which a series of fMRI images are time-locked to a stimulus presentation and averaged together over many trials. Again an event related potential (ERP) is a measured brain response that is directly the result of a thought or perception. Here the neuronal response of human visual cortex in normal healthy patients have been studied. The patients were asked to perform a visual three choice reaction task; from the relative response of each patient corresponding neuronal activity in visual cortex was imaged. The average number of neurons in the adult human primary visual cortex, in each hemisphere has been estimated at around 140 million. Statistical analysis of this experiment was done with SPM5(Statistical Parametric Mapping version 5) software. The result shows a robust design of imaging the neuronal activity of human visual cortex.

Keywords: Echo Planner Imaging, Event related Response, General Linear Model, Visual Neuronal Response.

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1317 A Digitally Programmable Voltage-mode Multifunction Biquad Filter with Single-Output

Authors: C. Ketviriyakit, W. Kongnun, C. Chanapromma, P. Silapan

Abstract:

This article proposes a voltage-mode multifunction filter using differential voltage current controllable current conveyor transconductance amplifier (DV-CCCCTA). The features of the circuit are that: the quality factor and pole frequency can be tuned independently via the values of capacitors: the circuit description is very simple, consisting of merely 1 DV-CCCCTA, and 2 capacitors. Without any component matching conditions, the proposed circuit is very appropriate to further develop into an integrated circuit. Additionally, each function response can be selected by suitably selecting input signals with digital method. The PSpice simulation results are depicted. The given results agree well with the theoretical anticipation.

Keywords: DV-CCCCTA, Voltage-mode, Multifunction filter

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1316 Business Intelligence for N=1 Analytics using Hybrid Intelligent System Approach

Authors: Rajendra M Sonar

Abstract:

The future of business intelligence (BI) is to integrate intelligence into operational systems that works in real-time analyzing small chunks of data based on requirements on continuous basis. This is moving away from traditional approach of doing analysis on ad-hoc basis or sporadically in passive and off-line mode analyzing huge amount data. Various AI techniques such as expert systems, case-based reasoning, neural-networks play important role in building business intelligent systems. Since BI involves various tasks and models various types of problems, hybrid intelligent techniques can be better choice. Intelligent systems accessible through web services make it easier to integrate them into existing operational systems to add intelligence in every business processes. These can be built to be invoked in modular and distributed way to work in real time. Functionality of such systems can be extended to get external inputs compatible with formats like RSS. In this paper, we describe a framework that use effective combinations of these techniques, accessible through web services and work in real-time. We have successfully developed various prototype systems and done few commercial deployments in the area of personalization and recommendation on mobile and websites.

Keywords: Business Intelligence, Customer Relationship Management, Hybrid Intelligent Systems, Personalization and Recommendation (P&R), Recommender Systems.

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1315 A Deep-Learning Based Prediction of Pancreatic Adenocarcinoma with Electronic Health Records from the State of Maine

Authors: Xiaodong Li, Peng Gao, Chao-Jung Huang, Shiying Hao, Xuefeng B. Ling, Yongxia Han, Yaqi Zhang, Le Zheng, Chengyin Ye, Modi Liu, Minjie Xia, Changlin Fu, Bo Jin, Karl G. Sylvester, Eric Widen

Abstract:

Predicting the risk of Pancreatic Adenocarcinoma (PA) in advance can benefit the quality of care and potentially reduce population mortality and morbidity. The aim of this study was to develop and prospectively validate a risk prediction model to identify patients at risk of new incident PA as early as 3 months before the onset of PA in a statewide, general population in Maine. The PA prediction model was developed using Deep Neural Networks, a deep learning algorithm, with a 2-year electronic-health-record (EHR) cohort. Prospective results showed that our model identified 54.35% of all inpatient episodes of PA, and 91.20% of all PA that required subsequent chemoradiotherapy, with a lead-time of up to 3 months and a true alert of 67.62%. The risk assessment tool has attained an improved discriminative ability. It can be immediately deployed to the health system to provide automatic early warnings to adults at risk of PA. It has potential to identify personalized risk factors to facilitate customized PA interventions.

Keywords: Cancer prediction, deep learning, electronic health records, pancreatic adenocarcinoma.

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1314 Effect of Spatially Correlated Disorder on Electronic Transport Properties of Aperiodic Superlattices (GaAs/AlxGa1-xAs)

Authors: F. Bendahma, S. Bentata, S. Cherid, A. Zitouni, S. Terkhi, T. Lantri, Y. Sefir, Z. F. Meghoufel

Abstract:

We examine the electronic transport properties in AlxGa1-xAs/GaAs superlattices. Using the transfer-matrix technique and the exact Airy function formalism, we investigate theoretically the effect of structural parameters on the electronic energy spectra of trimer thickness barrier (TTB). Our numerical calculations showed that the localization length of the states becomes more extended when the disorder is correlated (trimer case). We have also found that the resonant tunneling time (RTT) is of the order of several femtoseconds.

Keywords: Electronic transport properties, structural parameters, superlattice, transfer-matrix technique.

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1313 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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1312 Human Fall Detection by FMCW Radar Based on Time-Varying Range-Doppler Features

Authors: Xiang Yu, Chuntao Feng, Lu Yang, Meiyang Song, Wenhao Zhou

Abstract:

The existing two-dimensional micro-Doppler features extraction ignores the correlation information between the spatial and temporal dimension features. For the range-Doppler map, the time dimension is introduced, and a frequency modulation continuous wave (FMCW) radar human fall detection algorithm based on time-varying range-Doppler features is proposed. Firstly, the range-Doppler sequence maps are generated from the echo signals of the continuous motion of the human body collected by the radar. Then the three-dimensional data cube composed of multiple frames of range-Doppler maps is input into the three-dimensional Convolutional Neural Network (3D CNN). The spatial and temporal features of time-varying range-Doppler are extracted by the convolution layer and pool layer at the same time. Finally, the extracted spatial and temporal features are input into the fully connected layer for classification. The experimental results show that the proposed fall detection algorithm has a detection accuracy of 95.66%.

Keywords: FMCW radar, fall detection, 3D CNN, time-varying range-Doppler features.

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1311 On Chromaticity of Wheels

Authors: Zainab Yasir Al-Rekaby, Abdul Jalil M. Khalaf

Abstract:

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

Keywords: Chromatic Polynomial, Chromatically Equivalent, Chromatically Unique, Wheel.

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1310 An Interval-Based Multi-Attribute Decision Making Approach for Electric Utility Resource Planning

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

This paper presents an interval-based multi-attribute decision making (MADM) approach in support of the decision process with imprecise information. The proposed decision methodology is based on the model of linear additive utility function but extends the problem formulation with the measure of composite utility variance. A sample study concerning with the evaluation of electric generation expansion strategies is provided showing how the imprecise data may affect the choice toward the best solution and how a set of alternatives, acceptable to the decision maker (DM), may be identified with certain confidence.

Keywords: Decision Making, Power Generation, ElectricUtilities, Resource Planning.

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1309 Design of Variable Fractional-Delay FIR Differentiators

Authors: Jong-Jy Shyu, Soo-Chang Pei, Min-Han Chang

Abstract:

In this paper, the least-squares design of variable fractional-delay (VFD) finite impulse response (FIR) digital differentiators is proposed. The used transfer function is formulated so that Farrow structure can be applied to realize the designed system. Also, the symmetric characteristics of filter coefficients are derived, which leads to the complexity reduction by saving almost a half of the number of coefficients. Moreover, all the elements of related vectors or matrices for the optimal process can be represented in closed forms, which make the design easier. Design example is also presented to illustrate the effectiveness of the proposed method.

Keywords: Differentiator, variable fractional-delay filter, FIR filter, least-squares method, Farrow structure.

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1308 Attention Based Fully Convolutional Neural Network for Simultaneous Detection and Segmentation of Optic Disc in Retinal Fundus Images

Authors: Sandip Sadhukhan, Arpita Sarkar, Debprasad Sinha, Goutam Kumar Ghorai, Gautam Sarkar, Ashis K. Dhara

Abstract:

Accurate segmentation of the optic disc is very important for computer-aided diagnosis of several ocular diseases such as glaucoma, diabetic retinopathy, and hypertensive retinopathy. The paper presents an accurate and fast optic disc detection and segmentation method using an attention based fully convolutional network. The network is trained from scratch using the fundus images of extended MESSIDOR database and the trained model is used for segmentation of optic disc. The false positives are removed based on morphological operation and shape features. The result is evaluated using three-fold cross-validation on six public fundus image databases such as DIARETDB0, DIARETDB1, DRIVE, AV-INSPIRE, CHASE DB1 and MESSIDOR. The attention based fully convolutional network is robust and effective for detection and segmentation of optic disc in the images affected by diabetic retinopathy and it outperforms existing techniques.

Keywords: Ocular diseases, retinal fundus image, optic disc detection and segmentation, fully convolutional network, overlap measure.

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1307 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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