This book briefly covers internationally contributed chapters with artificial intelligence and applied mathematics-oriented background-details. Nowadays, the world is under attack of intelligent systems covering all fields to make them practical and meaningful for humans. In this sense, this edited book provides the most recent research on use of engineering capabilities for developing intelligent systems. The chapters are a collection from the works presented at the 2nd International Conference on Artificial Intelligence and Applied Mathematics in Engineering held within 09-10-11 October 2020 at the Antalya, Manavgat (Turkey). The target audience of the book covers scientists, experts, M.Sc. and Ph.D. students, post-docs, and anyone interested in intelligent systems and their usage in different problem domains. The book is suitable to be used as a reference work in the courses associated with artificial intelligence and applied mathematics.
Author(s): Jude Hemanth, Tuncay Yigit, Bogdan Patrut, Anastassia Angelopoulou
Series: Lecture Notes on Data Engineering and Communications Technologies, 76
Publisher: Springer
Year: 2021
Language: English
Pages: 799
City: Cham
Foreword
Foreword
Preface
Acknowledgement
International Conference on Artificial Intelligence and Applied Mathematics in Engineering 2020
Briefly About
Scope/Topics
Honorary Chairs
General Chair
Conference Chairs
Organizing Committee
Secretary
Accommodation/Venue Desk
Travel/Transportation
Web/Design/Conference Sessions
Scientific Committee
Keynote Speaks
Contents
Prediction of Liver Cancer by Artificial Neural Network
1 Introduction
2 Releated Works
3 Metodology
3.1 Artificial Neural Network
3.2 Training-Based Sampling
4 Experimental Results
5 Discussion and Conclusions
References
Remarks on the Limit-Circle Classification of Conformable Fractional Sturm-Liouville Operators
1 Introduction
2 Conformable Fractional Calculus
3 Main Result
References
Improving Search Relevance with Word Embedding Based Clusters
1 Introduction
2 Similar Studies
3 System Details
3.1 Processing of Data
3.2 Training of Word Embedding Models
3.3 Clustering
3.4 Elasticsearch
4 Conclusion
References
Predicting Suicide Risk in Turkey Using Machine Learning
1 Introduction
2 Material and Method
2.1 Data Representation
2.2 Normalization (z-Score)
2.3 Linear Regression (LR)
2.4 Measuring Analysis
3 Experimental Results
4 Conclusions, Suggestions and Future Work
References
Building an Open Source Big Data Platform Based on Milis Linux
1 Introduction
2 Related Works
3 Methodology
3.1 MILIS Linux Building System
3.2 Components of the Milis Big Data Platform
4 Conclusion
References
Machine Learning for the Diagnosis of Chronic Obstructive Pulmonary Disease and Photoplethysmography Signal – Based Minimum Diagnosis Time Detection
1 Introduction
2 Material and Method
2.1 Collection of Data
2.2 Signal Pre-processing
2.3 Feature Extraction
2.4 Feature Selection
2.5 The Decision Trees
2.6 Performance Evaluation Criteria
3 Results
4 Discussion
5 Conclusion
References
Diagnosis of Parkinson's Disease with Acoustic Sounds by Rule Based Model
1 Introduction
2 Materials and Methods
2.1 Data Set
2.2 Data Preprocessing
2.3 Feature Selection Algorithm
2.4 Classification
2.5 Performance Evaluation Criteria
3 Results
4 Discussion and Conclusion
5 Future Work
References
Text Classification Models for CRM Support Tickets
1 Introduction
2 Similar Works
3 System Details
References
SMOTE-Text: A Modified SMOTE for Turkish Text Classification
1 Introduction
2 Machine Learning
2.1 Text Representation for Classification
2.2 Machine Learning Techniques for Text Classification
3 Imbalanced Datasets in Machine Learning
3.1 Preparing Text Data for Machine Learning for Imbalanced Datasets
3.2 SMOTE Application of Synthetic Minority Oversampling Technique (SMOTe)
3.3 SMOTE-Text
4 Experiment
4.1 Data Collection and Preparation
4.2 Experimental Results and Evaluation
5 Conclusion and Suggestions
References
Development of Face Recognition System by Using Deep Learning and Face-Net Algorithm in the Operations Processes
1 Introduction
2 Face Recognition
3 Method
3.1 Deep Learning
3.2 Convolutional Neural Network
3.3 Face-Net
4 Study and Results and Discussion
5 Conclusions and Future Works
References
Mobile Assisted Travel Planning Software: The Case of Burdur
1 Introduction
2 Travelling Salesman Problem
3 Findings (Study)
4 Conclusions
References
Text-Based Fake News Detection via Machine Learning
1 Introduction
2 Relevant Literature
3 Model
3.1 Data and Methodology
3.2 Feature Selection
3.3 Recurrent Neural Networks (RNN)
4 Experimental Results and Discussion
4.1 Exploratory Data Analysis
5 Conclusion and Future Work
References
A Recommendation System for Article Submission for Researchers
1 Introduction
2 Background
3 Methodology
4 Result and Discussion
5 Conclusion
References
Optimal Power Flow Using Manta Ray Foraging Optimization
1 Introduction
2 OPF Formulation
2.1 Objective Function
2.2 Equality Constraints
2.3 Inequality Constraints
3 Manta Ray Foraging Optimization
3.1 Chain Foraging
3.2 Cyclone Foraging
3.3 Somersault Foraging
4 Simulation Results
4.1 Case 1: Classical OPF Problem
4.2 Case 2: OPF Problem Considering POZs
5 Conclusion
References
Optimal Coordination of Directional Overcurrent Relays Using Artificial Ecosystem-Based Optimization
1 Introduction
2 Formulation of Problem
2.1 Objective Function
2.2 Constraints
3 Artificial Ecosystem-Based Optimization Algorithm
3.1 Production
3.2 Consumption
3.3 Decomposition
4 Simulation Results
4.1 Experimental Settings
4.2 Model I: IEEE-3 Bus Test System
4.3 Model II: IEEE-4 Bus Test System
5 Conclusion
References
Performance Evaluation of Machine Learning Techniques on Flight Delay Prediction
1 Introduction
2 Literature Review on Machine Learning and Flight Delays
3 Methods
3.1 Artificial Neural Network
3.2 Extreme Gradient Boosting
3.3 Logistic Regression
3.4 Random Forest
3.5 CatBoost
3.6 Support Vector Machines (SVM)
4 Implementation of Machine Learning Methods on Flight Data
5 Conclusions and Future Work
References
Machine Breakdown Prediction with Machine Learning
1 Introduction
2 Predictive Maintenance
3 Predictive Maintenance with Artificial Intelligence
4 Application
5 Conclusions and Future Work
References
Prevention of Electromagnetic Impurities by Electromagnetics Intelligence
1 Introduction
2 Materials and Methods
3 Discussions and Suggestions
4 Conclusion
References
The Effect of Auscultation Areas on Nonlinear Classifiers in Computerized Analysis of Chronic Obstructive Pulmonary Disease
1 Introduction
2 Materials and Methods
2.1 Database
2.2 Empirical Wavelet Transform
2.3 Support Vector Machine
2.4 Multilayer Perceptron
3 Experimental Results
4 Conclusion
References
Least Square Support Vector Machine for Interictal Detection Based on EEG of Epilepsy Patients at Airlangga University Hospital Surabaya-Indonesia
1 Introduction
2 Theoretical Basis
2.1 Discrete Wavelet Transform (DWT)
2.2 Support Vector Machine (SVM)
2.3 Least Square Support Vector Machine (LS SVM)
2.4 Evaluation of Classification Performance
3 Methodology
4 Result and Suggestions
4.1 Signal Characteristics
4.2 Sub-band EEG Signal
4.3 Signal Feature Extraction
4.4 Classification
5 Conclusion
References
Generating Classified Ad Product Image Titles with Image Captioning
1 Introduction
2 Related Work
3 Methodology
3.1 Model Architecture
4 Experiments
4.1 Data Preprocessing
4.2 Experimental Results
5 Conclusion
References
Effectiveness of Genetic Algorithm in the Solution of Multidisciplinary Conference Scheduling Problem
1 Introduction
2 Problem Definition
2.1 Using Genetic Algorithm in Constricted Optimization Problems
2.2 Problem Constraints
2.3 Genetic Algorithm
2.4 Crossover
2.5 Mutation
2.6 Penalty Function and Fitness Value
3 Assessment of the Results
4 Conclusions and Suggestions
References
Analyze Performance of Embedded Systems with Machine Learning Algorithms
1 Introduction
2 Used Algorithms
2.1 Unsupervised Learning Algortihm
2.2 Supervised Learning Algorithms
3 Application of Algorithms
3.1 Importing Data and Visualizing the Data Set
3.2 Train and Test Data
3.3 Classification/Prediction
4 Experiments
5 Conclusion
References
Classification Performance Evaluation on Diagnosis of Breast Cancer
1 Introduction
2 Method
2.1 Datasets
2.2 Classification Algorithms
2.3 Performance Criteria
3 Experimental Results
4 Conclusion and Suggestions
References
Effective Factor Detection in Crowdfunding Systems
1 Introduction
2 Material and Method
3 Application
4 Conclusion and Suggestions
References
Predictive Analysis of the Cryptocurrencies’ Movement Direction Using Machine Learning Methods
1 Introduction
2 Material and Method
2.1 Linear Regression
2.2 Polynomial Regression
2.3 Support Vector Regression
2.4 Decision Tree Regression
2.5 Random Forest Regression
3 Statistical Evaluation Criteria of Fitting Model
3.1 R2 Method
3.2 Root Mean Square Error (RMSE)
3.3 Data Set
4 Results and Discussion
5 Conclusions and Suggestions
References
Sofware Quality Prediction: An Investigation Based on Artificial Intelligence Techniques for Object-Oriented Applications
1 Introduction
2 Related Works
3 Software Metrics and Dataset
3.1 Data Collection
3.2 Software Metrics
4 Machine Learning Techniques and Experiments
4.1 Decision Trees
4.2 Random Forest
4.3 Bayesian Classification
4.4 Rule-Based Classification
4.5 SVM – SMO, LibSVM, LibLINEAR
4.6 Logistic Regression
4.7 Bagging and Boosting
4.8 Artifical Neural Networks
4.9 Nearest Neighbors
5 Result and Evaluation
5.1 Performance Evaluation Results
6 Conclusion and Future Work
References
A Multi Source Graph-Based Hybrid Recommendation Algorithm
1 Introduction
2 Motivation
3 Multi-source Hybrid Recommendation Algorithm
4 Evaluation Measures
4.1 Hit-Ratio
4.2 Recall
4.3 Precision
5 Experimental Results and Datasets
6 Conclusion
References
Development of an Artificial Intelligence Based Computerized Adaptive Scale and Applicability Test
1 Introduction
2 Methodology
2.1 Workgroup
2.2 Analysis and Interpretation of Data
3 Findings
4 Discussion and Conclusion
5 Suggestions
References
Reduced Differential Transform Approach Using Fixed Grid Size for Solving Newell–Whitehead–Segel (NWS) Equation
1 Introduction
2 RDTM with Grid Size Solution
3 Application
4 Results and Discussion
5 Conclusions
References
A New Ensemble Prediction Approach to Predict Burdur House Prices
1 Introduction
2 Material and Methods
2.1 Burdur House Prices Dataset
2.2 Ensemble Prediction Approach
3 Findings
4 Conclusion
References
The Evidence of the “No Free Lunch” Theorems and the Theory of Complexity in Business Artificial Intelligence
1 Introduction
2 Background and Related Works
2.1 Business Artificial Intelligence (BAI)
2.2 Theory of Complexity and No Free Lunch Theorems in BAI
3 Problematic and Research Gap
3.1 Problematic of the Study
3.2 Scope of Related Research
4 Proposed Approach and Findings
4.1 Proposed Classifications
4.2 Discussion and Results
5 Conclusion and Future Works
References
Text Mining Based Decision Making Process in Kickstarter Platform
1 Introduction
2 Material and Method
3 Application
4 Conclusions and Suggestions
References
Deep Q-Learning for Stock Future Value Prediction
1 Introduction
2 Dataset
3 Assumptions
4 Method
5 The Combined DQN Method
6 Results
7 Conclusion
References
Effect of DoS Attacks on MTE/LEACH Routing Protocol-Based Wireless Sensor Networks
1 Introduction
1.1 Organization
2 Related Works
3 DoS Attacks
3.1 Physical Layer
3.2 Data-Link Layer
3.3 Network Layer
3.4 Transport Layer
4 Experimental Simulations and Results
5 Conclusions
References
On Connectivity-Aware Distributed Mobility Models for Area Coverage in Drone Networks
1 Introduction
2 Related Works
3 Mobility Models
3.1 Random Mobility Model
3.2 Distributed Pheromone Repel Mobility Model
3.3 Connectivity-Based Mobility Model
3.4 KHOPCA-Based Mobility Model
3.5 Connected Coverage Mobility Model
4 Performance Metrics
5 Simulation Results
6 Conclusion
References
Analysis of Movement-Based Connectivity Restoration Problem in Wireless Ad-Hoc and Sensor Networks
1 Introduction
2 Related Works
3 Problem Formulation
4 NP-Completeness of Movement Based Connectivity Restoration
5 Conclusion
References
Design of External Rotor Permanent Magnet Synchronous Reluctance Motor (PMSynRM) for Electric Vehicles
1 Introduction
2 Mathematical Expressions and Design of the External Rotor PMSynRM
3 Magnetic Analysis and Results of the Designed Motor
4 Conclusions
References
Support Vector Machines in Determining the Characteristic Impedance of Microstrip Lines
1 Introduction
2 Support Vector Machine
3 Microstrip Line
4 Classification for Microstrip Line
5 Regression for Microstrip Line
6 Conclusions
References
A New Approach Based on Simulation of Annealing to Solution of Heterogeneous Fleet Vehicle Routing Problem
1 Introduction
2 Simulated Annealing Problem
3 Problem Definition
3.1 Constraints in the Problem
3.2 Flexibilities in the Problem
4 Application
4.1 Using Annealing Simulation Algorithm in Problem Solution
4.2 Purpose Function Evaluation Method
5 Result
References
Microgrid Design Optimization and Control with Artificial Intelligence Algorithms for a Public Institution
1 Introduction
2 Related Works
3 Matlab/Simulink with an AC Microgrid Design
3.1 Artificial Intelligence Algorithm Designed for a Microgrid Control
3.2 AC Microgrid Simulink Model Simulation Results
4 Simulation and Optimization of a Microgrid with Homer
4.1 Simulation and Optimization of System Designed in Homer Program
5 Results
References
Determination of Vehicle Type by Image Classification Methods for a Sample Traffic Intersection in Isparta Province
1 Introduction
2 Material and Method
2.1 Material
2.2 Method
3 Research Findings
4 Results
References
Prediction of Heat-Treated Spruce Wood Surface Roughness with Artificial Neural Network and Random Forest Algorithm
1 Introduction
2 Material and Method
2.1 Provision of Experiment Samples and Conducting Experiments
2.2 Machine Learning Methods Used for Predictive Purposes
2.3 Creating the Data Set
2.4 Performance Measurement Metrics
3 Results
4 Conclusions
References
Design and Implementation of Microcontroller Based Hydrogen and Oxygen Generator Used Electrolysis Method
1 Introduction
2 Electrolysis
3 Hydrogen Energy
4 Designed Hydrogen and Oxygen Generator
4.1 Determination of Water Electrolysis Parameters with Experimental Analysis Method
4.2 Microcontroller Based Control Unit
4.3 Analog Measurement Circuits
4.4 Software
5 Results and Suggestions
References
ROSE: A Novel Approach for Protein Secondary Structure Prediction
1 Introduction
2 Methods
2.1 Problem Definition and Secondary Structure Labels
2.2 Predicting Secondary Structure Using ROSE
2.3 Combining 1D-BRNN and Dynamic Bayesian Networks
3 Application
4 Conclusions
References
A Deep Learning-Based IoT Implementation for Detection of Patients’ Falls in Hospitals
1 Introduction
1.1 Related Works
2 Materials and Methods
2.1 Dataset
2.2 Artificial Neural Networks
2.3 Recurrent Neural Networks
2.4 Long Short Term Memory (LSTM)
3 The LSTM Model for Fall Detection
3.1 Data Preprocessing
3.2 Model Architecture
3.3 The Proposed LSTM Model
3.4 Result and Discussion
4 Conclusion
References
Recognition of Vehicle Warning Indicators
1 Introduction
2 Vehicle Warning Light Symbols and Indicators
3 Windows Azure Cognitive Services
4 Experimental Analysis
4.1 Building Dataset
4.2 Experimental Setup and Performance Metrics
5 Conclusion
References
Time Series Analysis on EEG Data with LSTM
1 Introduction
2 Related Work
3 Material and Method
3.1 Dataset
3.2 LSTM (Long-Short Term Memory)
3.3 Performance Metric
4 Results
5 Conclusion
References
Gaussian Mixture Model-Based Clustering of Multivariate Data Using Soft Computing Hybrid Algorithm
1 Introduction
2 Method and Materials
2.1 Determining the Number of Components of Variables in Multivariate Data
2.2 Assignment of Expected Observations of Components by K-Means Algorithm
2.3 Comparison of K-Means and Gaussian Mixture Models in Determining Observations on Components
2.4 Determination of Number and Location of Cluster Centers in Normal Mixture Models
2.5 Numbers and Structure of Normal Mixture Models
2.6 Numbers of Grid Structured Normal Mixture Models and Genetic Algorithms
2.7 Determination of the Best Model According to Information Criteria Among Grid Structured Mixture Models
3 Results
3.1 Application of Proposed Hybrid Clustering Algorithm on Synthetic Data Set
4 Conclusion and Discussion
References
Design Optimization and Comparison of Brushless Direct Current Motor for High Efficiency Fan, Pump and Compressor Applications
1 Introduction
2 Design Optimization of BLDC
2.1 Artificial Intelligence
3 Optimization Results
4 FEA Verification of Optimal Design
5 FEA Verification of Optimal Design
6 Conclusion
References
Stability of a Nonautonomous Recurrent Neural Network Model with Piecewise Constant Argument of Generalized Type
1 Introduction and Preliminaries
1.1 Equilibrium Point and Existence-Uniqueness of Solutions
2 Uniform Asymptotic Stability of the Equilibrium Point
2.1 Lyapunov-Razumikhin Method
2.2 Lyapunov-Krasovskii Method
3 Example and Simulation
4 Conclusion
References
Dynamics of a Recurrent Neural Network with Impulsive Effects and Piecewise Constant Argument
1 Introduction
2 Preliminaries
2.1 Equilibrium Point
2.2 Existence and Uniqueness
2.3 Global Exponential Stability of the Equilibrium Point
3 An Example and a Simulation
4 Conclusion
References
A Pure Genetic Energy-Efficient Backbone Formation Algorithm for Wireless Sensor Networks in Industrial Internet of Things
1 Introduction
2 Background
3 Related Work
4 Proposed Method
5 Results
6 Conclusion
References
Fault Analysis in the Field of Fused Deposition Modelling (FDM) 3D Printing Using Artificial Intelligence
1 Introduction
2 Material and Method
2.1 Material
2.2 Method
3 Research Findings
4 Conclusions
References
Real-Time Maintaining of Social Distance in Covid-19 Environment Using Image Processing and Big Data
1 Introduction
2 Architectural Design and Methodology
2.1 Architecture
2.2 Video Stream
2.3 KubeFlow Pipelines
2.4 Data Stream
2.5 Data Storage
2.6 Query Dataset
2.7 Front-End
2.8 Notification
3 Conclusion
References
Determination of the Ideal Color Temperature for the Most Efficient Photosynthesis of Brachypodium Plant in Different Light Sources by Using Image Processing Techniques
1 Introduction
2 Materials and Methods
2.1 Photosynthesis from Plants
2.2 Brachypodium
2.3 Test Booth and Lighting System
2.4 Color Temperature of Light Sources
3 Application
4 Conclusion
References
Combination of Genetic and Random Restart Hill Climbing Algorithms for Vehicle Routing Problem
1 Introduction
2 Related Work
3 Formulation of the Problem
4 Algorithm Parameters Used
4.1 Genetic Algorithm
4.2 Random Restart Hill Climbing
5 Results from the Experiments
5.1 Results with Fitness Proportionate Selection
5.2 Uniform Distribution
5.3 Log-Normal Distribution
5.4 Exponential Distribution
6 Conclusion and Future Work
References
Reliability of Offshore Structures Due to Earthquake Load in Indonesia Water
1 Introduction
2 Objective and Scope of Research
3 Results and Discussion
3.1 Platform Data
3.2 Pushover Analysis
3.3 Seismic Analysis
3.4 Goodness of Fit
4 Conclusion
References
Unpredictable Oscillations of Impulsive Neural Networks with Hopfield Structure
1 Introduction
2 Preliminaries
3 Main Result
4 Examples
References
Performance Analysis of Particle Swarm Optimization and Firefly Algorithms with Benchmark Functions
1 Introduction
2 Literature Review
3 Particle Swarm Optimization (PSO)
4 Firefly Algorithm (FFA)
5 FFA Parameters
6 Test Functions
7 Test Results
8 Result and Discussion
References
Optimization in Wideband Code-Division Multiple Access Systems with Genetic Algorithm-Based Discrete Frequency Planning
1 Introduction
2 Material and Methods
2.1 Frequency Planning
2.2 Traffic Theorem
2.3 Genetic Algorithm
3 Application
4 Experimental Results
5 Results and Discussion
References
Deep Learning Based Classification Method for Sectional MR Brain Medical Image Data
1 Introduction
2 Related Work
3 Material and Method
3.1 Dataset
3.2 Image Processing
3.3 Deep Learning Model
3.4 Optimizer Parameter
4 Results
5 Conclusion
References
Analysis of Public Transportation for Efficiency
1 Introduction
2 Methodology
2.1 Route Efficiency - RE
2.2 Bus Stop Analysis
2.3 Hierarchical Clustering for Bus Stop Similarity
3 Results and Discussion
3.1 Route Efficiency - RE
3.2 Bus Stop Analysis
3.3 Hierarchical Clustering of Routes for Bus Stop Similarity
4 Conclusion
References
Methods for Trajectory Prediction in Table Tennis
1 Introduction
2 An Overview of the Trajectory Prediction Methods
2.1 Physics Modelling by Second Order Polynomial
2.2 Regression Learning with Experienced Data
2.3 Aerodynamics Model and Bouncing Model
2.4 EKF (Extended Kalman Filter) Supported Physical Model
2.5 Fuzzy Rectification for Spinning Ball
2.6 UKF (Unscented Kalman Filter) on Non-linear System and Spin Analyse with BP Neural Network
2.7 ADM (Aerodynamics Model) and RRM (Racket Rebound Model) Backward in Time
2.8 IELM (Improved Extreme Learning Machine) with Non-massive Data
2.9 E-SVR (e Support Vector Regression) Method
2.10 Weighted Least-Square Method
3 Performance Analysis of Methods
3.1 Accuracy
3.2 Time Usage
References
Emotion Analysis Using Deep Learning Methods
1 Introduction
2 Material Method
2.1 Material
2.2 Method
3 Research Findings
4 Results
References
A Nested Unsupervised Learning Model for Classification of SKU’s in a Transnational Company: A Big Data Model
1 Introduction
2 Materials and Methods
2.1 Description of the Data
2.2 Cluster Analysis
2.3 Architecture of the Proposed Model
3 Results
3.1 Cluster Analysis (Selection Between Hard and Soft Models)
3.2 Definition of Profiles by Iterations Within Each Group
4 Discontinuation SKU-Distributor
5 Conclusions and Recommendations
References
Identification of Trading Strategies Using Markov Chains and Statistical Learning Tools
1 Introduction
2 Materials and Methods
3 Markov Model
4 Generalized Additive Model (GAM)
5 Results
5.1 Markov Chain
5.2 Generalized Additive Model (GAM)
6 Conclusions
References
Estimation of the Stochastic Volatility of Oil Prices of the Mexican Basket: An Application of Boosting Monte Carlo Markov Chain Estimation
1 Introduction
2 Methodology
3 Stochastic Volatility Estimation by MCMC Using ASIS Algorithm
4 Conclusions
References
Optimization of the Input/Output Linearization Feedback Controller with Simulated Annealing and Designing of a Novel Stator Flux-Based Model Reference Adaptive System Speed Estimator with Least Mean Square Adaptation Mechanism
1 Introduction
2 Method and Material
2.1 Stator Flux-Based IM Model in Stator Stationary Reference Frame
2.2 Overwiev Simulated Annealing Algorithm
2.3 Overview of Particle Swarm Optimization
2.4 IOFLC Method
2.5 Novel Stator Flux-Based MRAS Speed Observer with LMS Adaptation Mechanism
3 Optimization Results and Estimation and Control Performance Simulation of MRAS with LMS Adaptation-Based Speed-Sensorles IOFLC-DTC of IM
4 Conclusions
References
Author Index