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.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

Gaba Receptor Gene Expression during Rat Liver Cell Proliferation and Its Function in Hepatocyte Cultures

The present thesis is an attempt to understand the role of GABA, GABAA and GABAB receptors in the regulation of liver cell proliferation using in vivo and in vitro models. The work also focuses on the brain GABAergic changes associated with normal and neoplastic cell growth in liver and to delineate its regulatory function. The investigation of mechanisms involving mitogenic models without cell necrosis may contribute our knowledge about both on cell growth, carcinogenesis, liver pathology and treatment. Objectives of the present study are, to induce controlled liver cell proliferation by partial hepatectomy and lead nitrate administration and uncontrolled cell proliferation by N-nitrosodiethylamine treatment in male Wistar rats, the changes in the content of GABA, GABAA,GABAB in various rat brain regions. To study the GABAA and GABAB receptor changes in brain stem, hypothalamus, cerebellum and cerebral cortex during the active cortex during the period of active DNA synthesis in liver of different experimental groups. The changes in GABAA and GABAB receptor function of the brain stem, hypothalamus and cerebellum play an important role sympathetic regulation of cell proliferation and neoplastic growth in liver. The decrease in GABA content in brain stem, hypothalamus and cerebellum during regeneration and neoplasia in liver. The time course of brain GABAergic changes was closely correlated with that of heptic DNA synthesis. The functional significance of these changes was further explored by studying the changes in GABAA and GABAB receptors in brain.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

A multiple-building diffraction attenuation function expressed in terms of UTD coefficients for microcellular communications

This work presents an explicit formulation for multiple- edge diffraction for mobile radiowave propagation in terms of uniform theory of diffraction (UTD) coefficients when a spherical incident wave is considered. This solution can be used in an UTD context and sharply reduces the computing time over existing formulation. Results can be applied in the planning of microcellular systems

Time evolution of the electron density and temperature in laser-produced plasmas from YBa2Cu3O7

Laser radiation at 1.06 µm from a pulsed Nd:YAG laser was focused onto a multielement YBa2Cu3O7 target in vacuum and the plasma thus generated was studied using time-resolved spectroscopic techniques. Line broadening of the Ba I emission line at 553.5 nm was monitored as a function of time elapsed after the incidence of a laser pulse on the target. Measured line profiles of barium species were used to infer the electron density and temperature, and the time evolution of these important plasma parameters has been worked out.

Spatial and time resolved analysis of CN bands in the laser induced plasma from graphite

Analysis of the emission bands of the CN molecules in the plasma generated from a graphite target irradiated with 1-06/~m radiation pulses from a Q-switched Nd:YAG laser has been done. Depending on the position of the sampled volume of the plasma plume, the intensity distribution in the emission spectra is found to change drastically. The vibrational temperature and population distribution in the different vibrational levels have been studied as function of distance from the target for different time delays with respect to the incidence of the laser pulse. The translational temperature calculated from time of flight is found to be higher than the observed vibrational temperature for CN molecules and the reason for this is explained.

Development of Time - Frequency Techniques for Sonar Applications

Sonar signal processing comprises of a large number of signal processing algorithms for implementing functions such as Target Detection, Localisation, Classification, Tracking and Parameter estimation. Current implementations of these functions rely on conventional techniques largely based on Fourier Techniques, primarily meant for stationary signals. Interestingly enough, the signals received by the sonar sensors are often non-stationary and hence processing methods capable of handling the non-stationarity will definitely fare better than Fourier transform based methods.Time-frequency methods(TFMs) are known as one of the best DSP tools for nonstationary signal processing, with which one can analyze signals in time and frequency domains simultaneously. But, other than STFT, TFMs have been largely limited to academic research because of the complexity of the algorithms and the limitations of computing power. With the availability of fast processors, many applications of TFMs have been reported in the fields of speech and image processing and biomedical applications, but not many in sonar processing. A structured effort, to fill these lacunae by exploring the potential of TFMs in sonar applications, is the net outcome of this thesis. To this end, four TFMs have been explored in detail viz. Wavelet Transform, Fractional Fourier Transfonn, Wigner Ville Distribution and Ambiguity Function and their potential in implementing five major sonar functions has been demonstrated with very promising results. What has been conclusively brought out in this thesis, is that there is no "one best TFM" for all applications, but there is "one best TFM" for each application. Accordingly, the TFM has to be adapted and tailored in many ways in order to develop specific algorithms for each of the applications.

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.

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Serotonin Receptor Gene Expression And Insulin Function In Streptozotocin Induced Diabetic Rats

Recent studies have established a fimctional correlation of serotonergic and adrenergic function in the brain regions with insulin secretion in diabetic rats (Vahabzadeh et al., 1995). Administration of 5-HT”. agonist 8-OH-DPAT to conscious rats caused an increase in blood glucose level. This increase in blood glucose is due to inhibition of insulin secretion by increased circulating EPI (Chaouloff et al., 1990a; Chaouloff et al., 1990d; Chaoulo1T& Jeanrenaud, 1987). The increase in EPI is brought about by increased sympathetic stimulation. This increase can lead to increased sympatho-medullary stimulation thereby inhibiting insulin release (Bauhelal & Mir, 1993, Bauhelal & Mir, 1990a; Chaouloffet al., 1990d). Also, studies have shown that Gi protein in the liver has been decreased in diabetes which will increase gluconeogenesis and glycogenolysis thereby causing hyperglycaemia (Pennington, 1987). Serotonergic control is suggested to exert different effects on insulin secretion according to the activation of different receptor subclasses (Pontiroli et al., 1975). In addition to this mechanism, the secretion of insulin is dependent on the turnover ratio of endogenous 5-hydroxy tryptophan (5-HTP) to 5-HT in the pancreatic islets (Jance er al., 1980). The reports so far stated does not explain the complete mechanism and the subclass of 5-HT receptors whose expression regulate insulin secretion in a diabetic state. Also, there is no report of a direct regulation of insulin secretion by 5-HT from the pancreatic islets even though there are reports stating that the pancreatic islets is a rich source of 5-HT (Bird et al., 1980). Therefore, in the present study the mechanism by which 5-HT and its receptors regulate insulin secretion from pancreatic [3-cells was investigated. Our results led to the following hypotheses by which 5-HT and its receptors regulate the insulin secretion.

Investigations on Stochastic Storage Systems with Positive Service Time

In this thesis the queueing-inventory models considered are analyzed as continuous time Markov chains in which we use the tools such as matrix analytic methods. We obtain the steady-state distributions of various queueing-inventory models in product form under the assumption that no customer joins the system when the inventory level is zero. This is despite the strong correlation between the number of customers joining the system and the inventory level during lead time. The resulting quasi-birth-anddeath (QBD) processes are solved explicitly by matrix geometric methods

Survival of multi-drug resistant enteropathogenic Escherichia coli and Salmonella paratyphi in Vembanadu lake as a function of saltwater barrier along southwest coast of India

The objective of the study was to evaluate the survival response of multi-drug resistant enteropathogenic Escherichia coli and Salmonella paratyphi to the salinity fluctuations induced by a saltwater barrier constructed in Vembanadu lake, which separates the lake into a freshwater dominated southern and brackish water dominated northern part. Therefore, microcosms containing freshwater, brackish water and microcosms with different saline concentrations (5, 10, 15, 20, 25 ppt) inoculated with E. coli/S. paratyphi were monitored up to 34 days at 20 and 30 WC. E. coli and S. paratyphi exhibited significantly higher (p <0.05) survival at 20 WC compared to 30 WC in all microcosms. Despite fresh/brackish water, E. coli and S. paratyphi showed prolonged survival up to 34 days at both temperatures. They also demonstrated better survival potential at all tested saline concentrations except 25 ppt where a significantly higher (p<0.0001) decay was observed. Therefore, enhanced survival exhibited by the multi-drug resistant enteropathogenic E. coli and S. paratyphi over a wide range of salinity levels suggest that they are able to remain viable for a very long time at higher densities in all seasons of the year in Vembanadu lake irrespective of saline concentrations, and may pose potential public health risks during recreational activities