Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Statistics of avalanches in martensitic transformations, II. Modelling

Using a scaling assumption, we propose a phenomenological model aimed to describe the joint probability distribution of two magnitudes A and T characterizing the spatial and temporal scales of a set of avalanches. The model also describes the correlation function of a sequence of such avalanches. As an example we study the joint distribution of amplitudes and durations of the acoustic emission signals observed in martensitic transformations [Vives et al., preceding paper, Phys. Rev. B 52, 12 644 (1995)].

Studies on underwater propagation development of programmable arrays

The thesis presented here includes the designing of underwater transducer arrays, taking into account the ‘interaction effects’ [30] among the closely packed radiators. Methods of minimizing the ‘interaction effects‘ by modifying the radiating aperture, are investigated. The need for this study arises as it is one of the important peculiar limitations that stands in the way of achieving maximum range of transmission of acoustic signals. Application of the modified array format for the generation of narrow beam low frequency sound waves, through nonlinear interactions, is discussed. Other techniques that can be advantageously exploited in array synthesis are also investigated

Studies on optical attenuation in sea water using dye laser and laser propagation in a turbulent medium

The central theme of the work presented in this thesis is a careful investigation of the factors influencing the attenuation of laser beam through sea water. The thesis presents a detailed report of the work done by the author on the attenuation studies in sea water and on laser propagation through a turbulent medium. The thesis contains six chapters which are more or less self-contained with separate abstracts and references. The first chapter is divided into two parts. The first part introduces the subject of laser propagation through sea water. It includes a brief description of optical properties of sea water followed by a review of the earlier works on attenuation studies in water. The second part gives the theoretical background of the problem of laser propagation through a turbulent medium.

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

Studies on some nonlinear schrodinger type equations describing pulse propagation through optical fibers

The discovery of the soliton is considered to be one of the most significant events of the twentieth century. The term soliton refers to special kinds of waves that can propagate undistorted over long distances and remain unaffected even after collision with each other. Solitons have been studied extensively in many fields of physics. In the context of optical fibers, solitons are not only of fundamental interest but also have potential applications in the field of optical fiber communications. This thesis is devoted to the theoretical study of soliton pulse propagation through single mode optical fibers.

Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters

Studies on sporulation and propagation in selected agarophytes

Studies on sporulation of four commercially important red (sea-weeds) algae ^(agarophytes) namely Gelidiella acerosa, Gracilaria corticata, G edulis and Hypnea musciformis growing in the vicinity of’ Mandapam coast were carried out from October 1981 to September 1983. During the two years of study; fruiting behavior in the natural population of these species was also investigated. Laboratory experiments were carried out with the four algae sea weeds to collect information on seasonal aspects of spore production and diurnal variation of spore shedding. Detailed studies were made under laboratory conditions to know the effects of some selected environmental factors such as desiccation, salinity, temperature, light intensity and photoperiod on spore output in Gelidiella acerosa, Gracilaria edulis and kypnea musciformis hydrological data were also collected from the inter-tial region around mandapam area. The result obtained on all the above aspects are presented in this thesis

Information discovery in distributed systems - A novel concept based on modelling of information elements

This thesis attempts to investigate the problems associated with such schemes and suggests a software architecture, which is aimed towards achieving a meaningful discovery. Usage of information elements as a modelling base for efficient information discovery in distributed systems is demonstrated with the aid of a novel conceptual entity called infotron. The investigations are focused on distributed systems and their associated problems. The study was directed towards identifying suitable software architecture and incorporating the same in an environment where information growth is phenomenal and a proper mechanism for carrying out information discovery becomes feasible. An empirical study undertaken with the aid of an election database of constituencies distributed geographically, provided the insights required. This is manifested in the Election Counting and Reporting Software (ECRS) System. ECRS system is a software system, which is essentially distributed in nature designed to prepare reports to district administrators about the election counting process and to generate other miscellaneous statutory reports.

Modelling of Ultraviolet and Vissible Emissions in Comets

Comets are the spectacular objects in the night sky since the dawn of mankind. Due to their giant apparitions and enigmatic behavior, followed by coincidental calamities, they were termed as notorious and called as `bad omens'. With a systematic study of these objects modern scienti c community understood that these objects are part of our solar system. Comets are believed to be remnant bodies of at the end of evolution of solar system and possess the material of solar nebula. Hence, these are considered as most pristine objects which can provide the information about the conditions of solar nebula. These are small bodies of our solar system, with a typical size of about a kilometer to a few tens of kilometers orbiting the Sun in highly elliptical orbits. The solid body of a comet is nucleus which is a conglomerated mixture of water ice, dust and some other gases. When the cometary nucleus advances towards the Sun in its orbit the ices sublimates and produces the gaseous envelope around the nucleus which is called coma. The gravity of cometary nucleus is very small and hence can not in uence the motion of gases in the cometary coma. Though the cometary nucleus is a few kilometers in size they can produce a transient, extensive, and expanding atmosphere with size several orders of magnitude larger in space. By ejecting gas and dust into space comets became the most active members of the solar system. The solar radiation and the solar wind in uences the motion of dust and ions and produces dust and ion tails, respectively. Comets have been observed in di erent spectral regions from rocket, ground and space borne optical instruments. The observed emission intensities are used to quantify the chemical abundances of di erent species in the comets. The study of various physical and chemical processes that govern these emissions is essential before estimating chemical abundances in the coma. Cameron band emission of CO molecule has been used to derive CO2 abundance in the comets based on the assumption that photodissociation of CO2 mainly produces these emissions. Similarly, the atomic oxygen visible emissions have been used to probe H2O in the cometary coma. The observed green ([OI] 5577 A) to red-doublet emission ([OI] 6300 and 6364 A) ratio has been used to con rm H2O as the parent species of these emissions. In this thesis a model is developed to understand the photochemistry of these emissions and applied to several comets. The model calculated emission intensities are compared with the observations done by space borne instruments like International Ultraviolet Explorer (IUE) and Hubble Space Telescope (HST) and also by various ground based telescopes.

Molecular cloning and homology modelling of a subtilisin-like serine protease from the marine fungus, Engyodontium album BTMFS10

An alkaline protease gene (Eap) was isolated for the first time from a marine fungus, Engyodontium album. Eap consists of an open reading frame of 1,161 bp encoding a prepropeptide consisting of 387 amino acids with a calculated molecular mass of 40.923 kDa. Homology comparison of the deduced amino acid sequence of Eap with other known proteins indicated that Eap encode an extracellular protease that belongs to the subtilase family of serine protease (Family S8). A comparative homology model of the Engyodontium album protease (EAP) was developed using the crystal structure of proteinase K. The model revealed that EAP has broad substrate specificity similar to Proteinase K with preference for bulky hydrophobic residues at P1 and P4. Also, EAP is suggested to have two disulfide bonds and more than two Ca2? binding sites in its 3D structure; both of which are assumed to contribute to the thermostable nature of the protein.

Molecular cloning and homology modelling of a subtilisin-like serine protease from the marine fungus, Engyodontium album BTMFS10

An alkaline protease gene (Eap) was isolated for the first time from a marine fungus, Engyodontium album. Eap consists of an open reading frame of 1,161 bp encoding a prepropeptide consisting of 387 amino acids with a calculated molecular mass of 40.923 kDa. Homology comparison of the deduced amino acid sequence of Eap with other known proteins indicated that Eap encode an extracellular protease that belongs to the subtilase family of serine protease (Family S8). A comparative homology model of the Engyodontium album protease (EAP) was developed using the crystal structure of proteinase K. The model revealed that EAP has broad substrate specificity similar to Proteinase K with preference for bulky hydrophobic residues at P1 and P4. Also, EAP is suggested to have two disulfide bonds and more than two Ca2? binding sites in its 3D structure; both of which are assumed to contribute to the thermostable nature of the protein.

Bivariate distributions with weighted marginals and reliablity modelling

In this paper, a family of bivariate distributions whose marginals are weighted distributions in the original variables is studied. The relationship between the failure rates of the derived and original models are obtained. These relationships are used to provide some characterizations of specific bivariate models

Modification of Polypropylene/High Density Polyethylene Blend Using Nanokaolinite Clay and E-Glass Fibre: Preparation, Characterization and Micromechanical Modelling

Upgrading two widely used standard plastics, polypropylene (PP) and high density polyethylene (HDPE), and generating a variety of useful engineering materials based on these blends have been the main objective of this study. Upgradation was effected by using nanomodifiers and/or fibrous modifiers. PP and HDPE were selected for modification due to their attractive inherent properties and wide spectrum of use. Blending is the engineered method of producing new materials with tailor made properties. It has the advantages of both the materials. PP has high tensile and flexural strength and the HDPE acts as an impact modifier in the resultant blend. Hence an optimized blend of PP and HDPE was selected as the matrix material for upgradation. Nanokaolinite clay and E-glass fibre were chosen for modifying PP/HDPE blend. As the first stage of the work, the mechanical, thermal, morphological, rheological, dynamic mechanical and crystallization characteristics of the polymer nanocomposites prepared with PP/HDPE blend and different surface modified nanokaolinite clay were analyzed. As the second stage of the work, the effect of simultaneous inclusion of nanokaolinite clay (both N100A and N100) and short glass fibres are investigated. The presence of nanofiller has increased the properties of hybrid composites to a greater extent than micro composites. As the last stage, micromechanical modeling of both nano and hybrid A composite is carried out to analyze the behavior of the composite under load bearing conditions. These theoretical analyses indicate that the polymer-nanoclay interfacial characteristics partially converge to a state of perfect interfacial bonding (Takayanagi model) with an iso-stress (Reuss IROM) response. In the case of hybrid composites the experimental data follows the trend of Halpin-Tsai model. This implies that matrix and filler experience varying amount of strain and interfacial adhesion between filler and matrix and also between the two fillers which play a vital role in determining the modulus of the hybrid composites.A significant observation from this study is that the requirement of higher fibre loading for efficient reinforcement of polymers can be substantially reduced by the presence of nanofiller together with much lower fibre content in the composite. Hybrid composites with both nanokaolinite clay and micron sized E-glass fibre as reinforcements in PP/HDPE matrix will generate a novel class of high performance, cost effective engineering material.