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.

Nitrifying Bioreactors Integrated into Shrimp and Prawn Hatchery Systems: Molecular Characterization of the Nitrifying Consortia,Reactor Kinetics, Modeling and Validation

National Centre for Aquatic Animal Health, Cochin University of Science and Technology

Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Mean Squared Residue Based Biclustering Algorithms for the Analysis of Gene Expression Data

Computational Biology is the research are that contributes to the analysis of biological data through the development of algorithms which will address significant research problems.The data from molecular biology includes DNA,RNA ,Protein and Gene expression data.Gene Expression Data provides the expression level of genes under different conditions.Gene expression is the process of transcribing the DNA sequence of a gene into mRNA sequences which in turn are later translated into proteins.The number of copies of mRNA produced is called the expression level of a gene.Gene expression data is organized in the form of a matrix. Rows in the matrix represent genes and columns in the matrix represent experimental conditions.Experimental conditions can be different tissue types or time points.Entries in the gene expression matrix are real values.Through the analysis of gene expression data it is possible to determine the behavioral patterns of genes such as similarity of their behavior,nature of their interaction,their respective contribution to the same pathways and so on. Similar expression patterns are exhibited by the genes participating in the same biological process.These patterns have immense relevance and application in bioinformatics and clinical research.Theses patterns are used in the medical domain for aid in more accurate diagnosis,prognosis,treatment planning.drug discovery and protein network analysis.To identify various patterns from gene expression data,data mining techniques are essential.Clustering is an important data mining technique for the analysis of gene expression data.To overcome the problems associated with clustering,biclustering is introduced.Biclustering refers to simultaneous clustering of both rows and columns of a data matrix. Clustering is a global whereas biclustering is a local model.Discovering local expression patterns is essential for identfying many genetic pathways that are not apparent otherwise.It is therefore necessary to move beyond the clustering paradigm towards developing approaches which are capable of discovering local patterns in gene expression data.A biclusters is a submatrix of the gene expression data matrix.The rows and columns in the submatrix need not be contiguous as in the gene expression data matrix.Biclusters are not disjoint.Computation of biclusters is costly because one will have to consider all the combinations of columans and rows in order to find out all the biclusters.The search space for the biclustering problem is 2 m+n where m and n are the number of genes and conditions respectively.Usually m+n is more than 3000.The biclustering problem is NP-hard.Biclustering is a powerful analytical tool for the biologist.The research reported in this thesis addresses the problem of biclustering.Ten algorithms are developed for the identification of coherent biclusters from gene expression data.All these algorithms are making use of a measure called mean squared residue to search for biclusters.The objective here is to identify the biclusters of maximum size with the mean squared residue lower than a given threshold. All these algorithms begin the search from tightly coregulated submatrices called the seeds.These seeds are generated by K-Means clustering algorithm.The algorithms developed can be classified as constraint based,greedy and metaheuristic.Constarint based algorithms uses one or more of the various constaints namely the MSR threshold and the MSR difference threshold.The greedy approach makes a locally optimal choice at each stage with the objective of finding the global optimum.In metaheuristic approaches particle Swarm Optimization(PSO) and variants of Greedy Randomized Adaptive Search Procedure(GRASP) are used for the identification of biclusters.These algorithms are implemented on the Yeast and Lymphoma datasets.Biologically relevant and statistically significant biclusters are identified by all these algorithms which are validated by Gene Ontology database.All these algorithms are compared with some other biclustering algorithms.Algorithms developed in this work overcome some of the problems associated with the already existing algorithms.With the help of some of the algorithms which are developed in this work biclusters with very high row variance,which is higher than the row variance of any other algorithm using mean squared residue, are identified from both Yeast and Lymphoma data sets.Such biclusters which make significant change in the expression level are highly relevant biologically.

Tropical Mesoscale Convective Systems and Associated Energetics : Observational and Modeling Studies

The main purpose of the thesis is to improve the state of knowledge and understanding of the physical structure of the TMCS and its short range prediction. The present study principally addresses the fine structure, dynamics and microphysics of severe convective storms.The structure and dynamics of the Tropical cloud clusters over Indian region is not well understood. The observational cases discussed in the thesis are limited to the temperature and humidity observations. We propose a mesoscale observational network along with all the available Doppler radars and other conventional and non—conventional observations. Simultaneous observations with DWR, VHF and UHF radars of the same cloud system will provide new insight into the dynamics and microphysics of the clouds. More cases have to be studied in detail to obtain climatology of the storm type passing over tropical Indian region. These observational data sets provide wide variety of information to be assimilated to the mesoscale data assimilation system and can be used to force CSRM.The gravity wave generation and stratosphere troposphere exchange (STE) processes associated with convection gained a great deal of attention to modem science and meteorologist. Round the clock observations using VHF and UHF radars along with supplementary data sets like DWR, satellite, GPS/Radiosondes, meteorological rockets and aircrafl observations is needed to explore the role of convection and associated energetics in detail.

Modeling premartensitic effects in Ni2MnGa: A mean-field and Monte Carlo simulation study

ic first-order transition line ending in a critical point. This critical point is responsible for the existence of large premartensitic fluctuations which manifest as broad peaks in the specific heat, not always associated with a true phase transition. The main conclusion is that premartensitic effects result from the interplay between the softness of the anomalous phonon driving the modulation and the magnetoelastic coupling. In particular, the premartensitic transition occurs when such coupling is strong enough to freeze the involved mode phonon. The implication of the results in relation to the available experimental data is discussed.

Precursor nanoscale modulations in ferromagnets: Modeling and thermodynamic characterization

Using a Ginzburg-Landau model for the magnetic degrees of freedom with coupling to disorder, we demonstrate through simulations the existence of stripelike magnetic precursors recently observed in Co-Ni-Al alloys above the Curie temperature. We characterize these magnetic modulations by means of the temperature dependence of local magnetization distribution, magnetized volume fraction, and magnetic susceptibility. We also obtain a temperature-disorder strength phase diagram in which a magnetic tweed phase exists in a small region between the paramagnetic and dipolar phases.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Modeling Of Work-Related Musculoskeletal Disorders In Chemical Process Industry In India

In this modern complex world, stress at work is found to be increasingly a common feature in day to day life. For the same reason, job stress is one of the active areas in occupational health and safety research for over last four decades and is continuing to attract researchers in academia and industry. Job stress in process industries is of concern due to its influence on process safety, and worker‘s safety and health. Safety in process (chemical and nuclear material) industry is of paramount importance, especially in a thickly populated country like India. Stress at job is the main vector in inducing work related musculoskeletal disorders which in turn can affect the worker health and safety in process industries. In view of the above, the process industries should try to minimize the job stress in workers to ensure a safe and healthy working climate for the industry and the worker. This research is mainly aimed at assessing the influence of job stress in inducing work related musculoskeletal disorders in chemical process industries in India

Theoretical modeling of photon and electron-stimulated Na and K desorption from SiO2

The mechanism of generation of atomic Na and K from SiO2 samples has been studied using explicitly correlated wave function and density functional theory cluster calculations. Possible pathways for the photon and electron stimulated desorption of Na and K atoms from silicates are proposed, thus providing new insight on the generation of the tenuous Na and K atmosphere of the Moon.

‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Use of Novel Algorithms MAJE4 and MACJER-320 for Achieving Confidentiality and Message Authentication in SSL & TLS.

Extensive use of the Internet coupled with the marvelous growth in e-commerce and m-commerce has created a huge demand for information security. The Secure Socket Layer (SSL) protocol is the most widely used security protocol in the Internet which meets this demand. It provides protection against eaves droppings, tampering and forgery. The cryptographic algorithms RC4 and HMAC have been in use for achieving security services like confidentiality and authentication in the SSL. But recent attacks against RC4 and HMAC have raised questions in the confidence on these algorithms. Hence two novel cryptographic algorithms MAJE4 and MACJER-320 have been proposed as substitutes for them. The focus of this work is to demonstrate the performance of these new algorithms and suggest them as dependable alternatives to satisfy the need of security services in SSL. The performance evaluation has been done by using practical implementation method.

Analyzing and Modeling a Multiparty Outsourcing Environment.

This paper discusses the complexities involved in managing and monitoring the delivery of IT services in a multiparty outsourcing environment. The complexities identified are grouped into four categories and are tabulated. A discussion on an attempt to model a multiparty outsourcing scenario using UML is also presented and explained using an illustration. Such a model when supplemented by a performance evaluation tool can enable an organization to manage the provision of IT services in a multiparty outsourcing environment more effectively

SPATIAL CLUSTERING ALGORITHMS-AN OVERVIEW.

An Overview of known spatial clustering algorithms The space of interest can be the two-dimensional abstraction of the surface of the earth or a man-made space like the layout of a VLSI design, a volume containing a model of the human brain, or another 3d-space representing the arrangement of chains of protein molecules. The data consists of geometric information and can be either discrete or continuous. The explicit location and extension of spatial objects define implicit relations of spatial neighborhood (such as topological, distance and direction relations) which are used by spatial data mining algorithms. Therefore, spatial data mining algorithms are required for spatial characterization and spatial trend analysis. Spatial data mining or knowledge discovery in spatial databases differs from regular data mining in analogous with the differences between non-spatial data and spatial data. The attributes of a spatial object stored in a database may be affected by the attributes of the spatial neighbors of that object. In addition, spatial location, and implicit information about the location of an object, may be exactly the information that can be extracted through spatial data mining