Modeling and Analysis of Some Heavy Tailed Time Series

The thesis has covered various aspects of modeling and analysis of finite mean time series with symmetric stable distributed innovations. Time series analysis based on Box and Jenkins methods are the most popular approaches where the models are linear and errors are Gaussian. We highlighted the limitations of classical time series analysis tools and explored some generalized tools and organized the approach parallel to the classical set up. In the present thesis we mainly studied the estimation and prediction of signal plus noise model. Here we assumed the signal and noise follow some models with symmetric stable innovations.We start the thesis with some motivating examples and application areas of alpha stable time series models. Classical time series analysis and corresponding theories based on finite variance models are extensively discussed in second chapter. We also surveyed the existing theories and methods correspond to infinite variance models in the same chapter. We present a linear filtering method for computing the filter weights assigned to the observation for estimating unobserved signal under general noisy environment in third chapter. Here we consider both the signal and the noise as stationary processes with infinite variance innovations. We derived semi infinite, double infinite and asymmetric signal extraction filters based on minimum dispersion criteria. Finite length filters based on Kalman-Levy filters are developed and identified the pattern of the filter weights. Simulation studies show that the proposed methods are competent enough in signal extraction for processes with infinite variance.Parameter estimation of autoregressive signals observed in a symmetric stable noise environment is discussed in fourth chapter. Here we used higher order Yule-Walker type estimation using auto-covariation function and exemplify the methods by simulation and application to Sea surface temperature data. We increased the number of Yule-Walker equations and proposed a ordinary least square estimate to the autoregressive parameters. Singularity problem of the auto-covariation matrix is addressed and derived a modified version of the Generalized Yule-Walker method using singular value decomposition.In fifth chapter of the thesis we introduced partial covariation function as a tool for stable time series analysis where covariance or partial covariance is ill defined. Asymptotic results of the partial auto-covariation is studied and its application in model identification of stable auto-regressive models are discussed. We generalize the Durbin-Levinson algorithm to include infinite variance models in terms of partial auto-covariation function and introduce a new information criteria for consistent order estimation of stable autoregressive model.In chapter six we explore the application of the techniques discussed in the previous chapter in signal processing. Frequency estimation of sinusoidal signal observed in symmetric stable noisy environment is discussed in this context. Here we introduced a parametric spectrum analysis and frequency estimate using power transfer function. Estimate of the power transfer function is obtained using the modified generalized Yule-Walker approach. Another important problem in statistical signal processing is to identify the number of sinusoidal components in an observed signal. We used a modified version of the proposed information criteria for this purpose.

An Online Character Recognition System to Convert Grantha Script to Malayalam

This paper presents a novel approach to recognize Grantha, an ancient script in South India and converting it to Malayalam, a prevalent language in South India using online character recognition mechanism. The motivation behind this work owes its credit to (i) developing a mechanism to recognize Grantha script in this modern world and (ii) affirming the strong connection among Grantha and Malayalam. A framework for the recognition of Grantha script using online character recognition is designed and implemented. The features extracted from the Grantha script comprises mainly of time-domain features based on writing direction and curvature. The recognized characters are mapped to corresponding Malayalam characters. The framework was tested on a bed of medium length manuscripts containing 9-12 sample lines and printed pages of a book titled Soundarya Lahari writtenin Grantha by Sri Adi Shankara to recognize the words and sentences. The manuscript recognition rates with the system are for Grantha as 92.11%, Old Malayalam 90.82% and for new Malayalam script 89.56%. The recognition rates of pages of the printed book are for Grantha as 96.16%, Old Malayalam script 95.22% and new Malayalam script as 92.32% respectively. These results show the efficiency of the developed system

Face Recognition using Probabilistic Neural Networks

In this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results

Face Recognition using Probabilistic Neural Networks

n this paper we address the problem of face detection and recognition of grey scale frontal view images. We propose a face recognition system based on probabilistic neural networks (PNN) architecture. The system is implemented using voronoi/ delaunay tessellations and template matching. Images are segmented successfully into homogeneous regions by virtue of voronoi diagram properties. Face verification is achieved using matching scores computed by correlating edge gradients of reference images. The advantage of classification using PNN models is its short training time. The correlation based template matching guarantees good classification results.

Studies on the use of Nanokaolin, MWCNT and Graphene in NBR and SBR

The current research investigates the possibility of using unmodified and modified nanokaolin, multiwalled carbon nanotube (MWCNT) and graphene as fillers to impart enhancement in mechanical, thermal, and electrical properties to the elastomers. Taking advantage of latex blending method, nanoclay, MWCNT and graphene dispersions, prepared by ultra sound sonication are dispersed in polymer latices. The improvement in material properties indicated better interaction between filler and the polymer.MWCNT and graphene imparted electrical conductivity with simultaneous improvement in mechanical properties. Layered silicates prepared by microwave method also significantly improve the mechanical properties of the nanocomposites. The thesis entitled ‘Studies on the use of Nanokaolin, MWCNT and Graphene in NBR and SBR’ consists of ten chapters. The first chapter is a concise introduction of nanocomposites, nanofillers, elastomeric matrices and applications of polymer nanocomposites. The state-of-art research in elastomer based nanocomposites is also presented. At the end of this chapter the main objectives of the work are mentioned. Chapter 2 outlines the specifications of various materials used, details of experimental techniques employed for preparing and characterizing nanocomposites. Chapter3 includes characterization of the nanofillers, optimsation of cure time of latex based composites and the methods used for the preparation of latex based and dry rubber based nanocomposites. Chapter4 presents the reinforcing effect of the nanofillers in XNBR latex and the characterization of the nanocomposites. Chapter5 comprises the effect of nanofillers on the properties of SBR latex and their characterization Chapter 6 deals with the study of cure characteristics, mechanical and thermal properties and the characterization of NBR based nanocomposites. Chapter7 is the microwave studies of MWCNT and graphene filled elastomeric nanocomposites. Chapter 8 gives details of the preparation of layered silicates, their characterization and use in different elastomeric matrices. Chapter 9 is the study of mechanical properties of nanoclay incorporated nitrile gloves .Chapter 10 presents the summary and conclusions of the investigation.