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.

Soft Computing Approach for Optimization of siRNA Efficiency Prediction for Post-transcriptional Gene Silencing

Post-transcriptional gene silencing by RNA interference is mediated by small interfering RNA called siRNA. This gene silencing mechanism can be exploited therapeutically to a wide variety of disease-associated targets, especially in AIDS, neurodegenerative diseases, cholesterol and cancer on mice with the hope of extending these approaches to treat humans. Over the recent past, a significant amount of work has been undertaken to understand the gene silencing mediated by exogenous siRNA. The design of efficient exogenous siRNA sequences is challenging because of many issues related to siRNA. While designing efficient siRNA, target mRNAs must be selected such that their corresponding siRNAs are likely to be efficient against that target and unlikely to accidentally silence other transcripts due to sequence similarity. So before doing gene silencing by siRNAs, it is essential to analyze their off-target effects in addition to their inhibition efficiency against a particular target. Hence designing exogenous siRNA with good knock-down efficiency and target specificity is an area of concern to be addressed. Some methods have been developed already by considering both inhibition efficiency and off-target possibility of siRNA against agene. Out of these methods, only a few have achieved good inhibition efficiency, specificity and sensitivity. The main focus of this thesis is to develop computational methods to optimize the efficiency of siRNA in terms of “inhibition capacity and off-target possibility” against target mRNAs with improved efficacy, which may be useful in the area of gene silencing and drug design for tumor development. This study aims to investigate the currently available siRNA prediction approaches and to devise a better computational approach to tackle the problem of siRNA efficacy by inhibition capacity and off-target possibility. The strength and limitations of the available approaches are investigated and taken into consideration for making improved solution. Thus the approaches proposed in this study extend some of the good scoring previous state of the art techniques by incorporating machine learning and statistical approaches and thermodynamic features like whole stacking energy to improve the prediction accuracy, inhibition efficiency, sensitivity and specificity. Here, we propose one Support Vector Machine (SVM) model, and two Artificial Neural Network (ANN) models for siRNA efficiency prediction. In SVM model, the classification property is used to classify whether the siRNA is efficient or inefficient in silencing a target gene. The first ANNmodel, named siRNA Designer, is used for optimizing the inhibition efficiency of siRNA against target genes. The second ANN model, named Optimized siRNA Designer, OpsiD, produces efficient siRNAs with high inhibition efficiency to degrade target genes with improved sensitivity-specificity, and identifies the off-target knockdown possibility of siRNA against non-target genes. The models are trained and tested against a large data set of siRNA sequences. The validations are conducted using Pearson Correlation Coefficient, Mathews Correlation Coefficient, Receiver Operating Characteristic analysis, Accuracy of prediction, Sensitivity and Specificity. It is found that the approach, OpsiD, is capable of predicting the inhibition capacity of siRNA against a target mRNA with improved results over the state of the art techniques. Also we are able to understand the influence of whole stacking energy on efficiency of siRNA. The model is further improved by including the ability to identify the “off-target possibility” of predicted siRNA on non-target genes. Thus the proposed model, OpsiD, can predict optimized siRNA by considering both “inhibition efficiency on target genes and off-target possibility on non-target genes”, with improved inhibition efficiency, specificity and sensitivity. Since we have taken efforts to optimize the siRNA efficacy in terms of “inhibition efficiency and offtarget possibility”, we hope that the risk of “off-target effect” while doing gene silencing in various bioinformatics fields can be overcome to a great extent. These findings may provide new insights into cancer diagnosis, prognosis and therapy by gene silencing. The approach may be found useful for designing exogenous siRNA for therapeutic applications and gene silencing techniques in different areas of bioinformatics.

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576