Application of Multivariate Statistical Analysis for the Detection of Structural Changes in the Series of Monitoring Data

A new approach to the study of time series by the projection pursuit methods is described. The ideas are illustrated on the time series of the monitoring of the environment and climate: (a) on time series of anomalies of global mean annual temperature -- the main climatological parameter; (b) on time series of atmospheric CO2 concentrations -- the main greenhouse gases; (c) on time series of vegetation index (NDVI) -- the main global characteristic of biota activity on the satellite data. With the aid of the shift operator for time signal, we construct a curve in n-dimensional Euclidian space (shift operator and integer n are the parameters of method). So an analysis of a time series is reduced to the analysis of the most informative projections [for example, by the criterion of factor analysis or spectral analysis (discrete Fourie analysis)] of the corresponding n-dimensional curve. We show that the comparison of such projections for model-test time series with the projection of the time series under investigation gives an effective way of finding the structural changes of the monitoring time series. For example, the case of the Hansen-Lebedeff time series of anomalies of the global mean annual temperature (see Rends 'go), shows that the structure of the series in the interval from 1920 until 1950 essentially differs from the structure on the intervals 1880-1920 and 1950-1987. For the series of CO2 on the Mauna Loa and Barrow monitoring stations, we obtained dynamics of the amplitudes of the year and semi-year cycles. We give the construction of a nonparametric estimation of a model of the initial time series using k-dimensional projection of n-dimensional curve. As a consequence, for example, we found the main components of the CO2 time series and obtained the models of the yearly behaviors of NDVI time series which permit one to carry out statistically stable classification of ecosystems by ecotypes and to describe dynamics of the separate ecosystems. Thus it is proposed a tool for the creation of the statistical description of the current state of the given monitoring series in the form of geometrical image. These geometrical images permit us to analyze the anomalies in the monitoring series in the terms of deviation of these images. As it follows from the examples given below such a method of the analysis of monitoring data is an effective method. Between the theoretical let us stress the following: we show how the methods of the analysis of the time series widely used in statistical treatment of monitoring data could also be used in our approach as the tools of the projections pursuit for comparing the images of the curves of the signal under investigation with the curves of the corresponding signals; it is shown that the proposed approach permits us to join in a united method the achievement of the theory of operators of a generalized shift and exploratory analysis on the basis of the projection pursuit

Theory of zone radiometry

A spectroscopic instrumentation system was developed which was used to measure temperature and concentration distributions in axisymmetric and two dimensional combusting flows. This measurement technique is known as zone radiometry

Wavelet-based simulation of geological variables

This thesis introduces a number of conditional simulation algorithms using wavelet bases. These make use of two orthogonal wavelet bases, the Haar and the Db2 bases. Firstly, two single-level algorithms are introduced, HSIM: with the Haar basis and DB2SIM with the Db2 basis. HSIM reproduces the histogram and semivariogram model of isotropic samples but not the semivariogrnm model of anisotropic samples. DB2SIM reproduces the histogram and semivariogram model in both the isotropic and anisotropic cases but, because of the conditioning method employed, is not as computationally efficient as we would wish. Because of the limitations of HSIM and Db2SIM two multi-level wavelet-based conditional simulation algorithms PWSIM and DWSIM have then been developed. In PWSIM, the conditional realisations are obtained by post-processing non-conditional realisations generated via an available non-conditional simulation algorithm using kriging. In DWSJM the data are conditioned directly via properties of the discrete wavelet transform. Because of the conditioning method, DWSIM is faster than PWSIM. The performance of PWIM and DWSIM with respect to the Haar and the Db2 wavelet bases is assessed via the local and global accuracy of the results. Both quantitative and visual assessments indicate that, for both wavelet bases, the realisations obtained via PWSIM have more variability than those obtained via DWSIM. If the Haar basis is used, PWSIM and DWSIM perform equally well. If the Db2 basis is used then PWSIM performance is much better than DWSIM performance. For both PWSIM and DWSIM, the use of the Db2 basis rather than the Haar basis increases the computational effort without producing a comparable increase in algorithm performance. In PWSIM the use of the Db2 basis slightly improves algorithm performance but the use of the Db2 basis in DWSIM decreases algorithm performance. A performance comparison between DWSIM using the Haar basis and the commonly used conditional simulation algorithm SGSIM shows that DWSIM produces results that are at least as good as those obtained by SGSIM but with less computational effort. The computational advantage of DWSIM over SGSIM is especially pronounced when a large number of realisations are simulated. In addition, the result obtained via DWSIM does not depend on user defined parameters as is the case in both SGSIM and PWSIM. The final result here is a (Haar) wavelet-based conditional simulation algorithm DWSIM that performs well in both the isotropic and the anisotropic cases and, particularly when simulating a large number of realisations, is much faster than the standard algorithm in common use

Traces of Extra Dimensions in Cosmology

In this thesis, we discuss the observational consequences of extra dimensions on cosmological phenomena. We begin with an overview of extra dimensions, from the initial ideas of Kaluza and Klein to the more recent concept of braneworld models and in particular review the cosmological aspects of the DGP braneworld model, which can produce late time acceleration. We then go on to consider the asymmetric brane model, comparing its cosmology to the standard concordance and DGP models and showing how the asymmetric model can be considered a one-parameter extension of the DGP model over a range of relevant physical scales. Using type Ia supernovae data and the cosmic microwave background shift parameter, the effect of this new parameter on the expansion history of the universe is considered. We then turn our attention to cosmic string loops, which emit bursts of gravitational radiation, produced by cusps and kinks on the loops. We investigate the kinematic effect extra dimensions will have on these gravitational wave bursts and find that the effects of the additional dimensions are more pronounced for cusps than for kinks: cusps are rounded off and their probability of formation is reduced, however, the probability of kink formation is unchanged. Finally, we recompute the gravitational wave bursts taking the various factors into account and look at the implications of this recalculation for the LIGO and LISA gravitational wave detectors, find that both signals, and in particular the cusp signal, have a potentially significant damping, and consider the implications for the detection of extra dimensions

Plasma Dynamics

Contains reports on three research projects.National Science Foundation (Grant G-9330)United States Air Force, Air Force Cambridge Research Center (Contract AF19(604)-5992)United States ArmyUnited States Air Force (Contract AF19(604)-7400)Lincoln Laboratory (Purchase Order B-00306)Flight Accessories Laboratory, Wright-Patterson Air Force Base (WADD Contract AF33(616)-7624)United States Air Force, Air Force Cambridge Research Laboratories (Contract AF19(604)-4551)United States NavyUnited States Atomic Energy Commission (Contract AT(30-1)-1842