Matrix-State Particle Filter for Wishart Stochastic Volatility Processes

This work deals with multivariate stochastic volatility models, which account for a time-varying variance-covariance structure of the observable variables. We focus on a special class of models recently proposed in the literature and assume that the covariance matrix is a latent variable which follows an autoregressive Wishart process. We review two alternative stochastic representations of the Wishart process and propose Markov-Switching Wishart processes to capture different regimes in the volatility level. We apply a full Bayesian inference approach, which relies upon Sequential Monte Carlo (SMC) for matrix-valued distributions and allows us to sequentially estimate both the parameters and the latent variables.Multivariate Stochastic Volatility; Matrix-State Particle Filters; Sequential Monte Carlo; Wishart Processes, Markov Switching.

Bayesian Inference on Dynamic Models with Latent Factors

In time series analysis, latent factors are often introduced to model the heterogeneous time evolution of the observed processes. The presence of unobserved components makes the maximum likelihood estimation method more difficult to apply. A Bayesian approach can sometimes be preferable since it permits to treat general state space models and makes easier the simulation based approach to parameters estimation and latent factors filtering. The paper examines economic time series models in a Bayesian perspective focusing, through some examples, on the extraction of the business cycle components. We briefly review some general univariate Bayesian dynamic models and discuss the simulation based techniques, such as Gibbs sampling, adaptive importance sampling and finally suggest the use of the particle filter, for parameter estimation and latent factor extraction.Bayesian Dynamic Models, Simulation Based Inference, Particle Filters, Latent Factors, Business Cycle

The observability of isolated neutron stars and black holes.

The detection of old neuron stars and black holes in isolation is one of the cornerstones of compact object astrophysics. However, forty years after the first pioneering studies, no succesful candidates have been found to confirm the early predictions, making the search for old isolated compact objects a still open and intriguing subject. The scope of this thesis is thus to investigate the observability of isolated neutron stars and black holes with the final objective of defining new possible strategies for the long sought detection of these elusive objects. The thesis is organized as follows. In Chapter 1, after a short discussion on the origin of neuron stars and stellar mass black holes in isolation, I summarize the results of past efforts made to constrain their observational properties. In Chapter 2 I tackle with the dynamics of isolated neutron stars. I describe the set up of a numerical Monte Carlo code, named Population Synthesis of Compact Objects (PSYCO in brief), developed as part of the PhD project. I then present the results of the simulation with particular emphasis for statistical properties of neutron stars in the Galactic disk and in the solar neighbourhood. These first results will be used as base to explore alternative methods to detect old neutron stars and black holes. It should be noted that, following the standard practice, these first results are obtained considering only neutron stars born in the disk of the Milky Way. As it will be shown in Chapter 3, the contribution of neutron stars, and black holes, born in the Galactic bulge cannot be neglected since they could represent the majority of detectable objects. In Chapter 3 the feasibility of microlensing as a technique to detect isolated neutron stars and black holes is explored, making use of the results illustrated in the previous Chapter. After an overview of results obtained so far by the several surveys, I describe the basic microlensing quantities and expressions. I then describe the models adopted in my work for the distribution of bulge and disk stars, to which the contribution of neutron stars and black oles is then compared to. I compare the optical depth and event rate due to neutron stars and black holes with that of normal stars. Also, I study the distribution of event time scales in both cases. After the results reported in Chapter 3, in Chapter 4 I present a systematic cross correlation analysis of microlensing events with the catalogues of X-rays sources of the XMM-Newton and Chandra satellites, which appeared recently. I report the results of the cross correlation and the properties of a source resulting from the cross correlation procedure. Finally, in Chapter 5 I review the results of my PhD project and draw the final conclusion. I also discuss possible future developments

Defect Detection and Thickness Mapping of Passivation Layers on Integrated Circuits Using Energy Dispersive X-Ray Analysis and Image Processing Techniques

The relative thickness of passivation layers has been mapped for integrated circuits by utilizing the penetration voltage method, in conjunction with energy dispersive x-ray analysis (EDXA) and a scanning electron microscope (SEM), to detect defects and map film thickness. The thickness mapping technique was evaluated for area coverage and correlated to size of defective areas. The purpose of this study was to determine optimal operational conditions for fast and accurate defect detection on an integrated circuit for failure analysis and non-destructive process evaluation. Image processing was required to enhance the acquired map and to obtain a calibrated image for relative comparison of thickness non-uniformity. Once the defect is detected, linescan and spot measurements can be used to obtain more accurate characterization of the defect areas. Considerable improvement in the detection and characterization of thickness and hole defects in the passivation layers on integrated circuit devices can be obtained with the use of this method

Comparative analysis of numerical integration techniques

When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson\u27s rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by √1-x 2, or as a function g(x) times (1-x)α (l+x)ß , where α and ß are some real numbers \u3e1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and Legendre- Gauss quadrature are respectively quite useful. If the integrand can not be expressed as f(x)/ √1-x 2 or as g(x)·(1-x) α ·(1+x) ß or as h(x) ·(1) then the Romberg method should be used. If the interval of integration is [0,∞] or [-∞,∞], then the Laguerre-Gauss and the Hermite-Gauss methods respectively are generally quite useful. The results of this study indicate that the quadrature formula to use in a given situation is dependent upon the interval of integration and the integrand. However, the results also indicate certain guide lines for choosing the type of quadrature formula to use in a given situation --Abstract, page iii

Measurement of Film Thickness on Integrated Circuits using Energy Dispersive X-Ray Analysis (EDXA)

The need for a rapid, non-destructive failure analysis of complex integrated circuits has led to the use of energy dispersive x-ray analysis (EDXA), to measure the localized thickness of Si02 and Al films on integrated circuits, by detecting the penetration threshold of the electron beam through the film. The accuracy (10%-20%) is determined by actual Scanning Electron Microscope (SEM) measurements, traceable to a secondary length standard, of the film thicknesses of sectioned samples. In contrast, another SEM based thickness measurement technique, such as Yakowitz-Newbury method, gave results that were 50-100% larger, required higher accelerating voltage that would damage the integrated circuit and took longer to setup/perform measurement. Typically, the thickness of the films range from 0.3 to 1.5 microns and thee-beam energy varies from 4 keV to 20 keV

A study of the long term variability of RX J1856.5-3754 with XMM-Newton

We report on a detailed spectral analysis of all the available XMM-Newton data of RX J1856.5-3754, the brightest and most extensively observed nearby, thermally emitting neutron star. Very small variations (~1-2%) in the single-blackbody temperature are detected, but are probably due to an instrumental effect, since they correlate with the position of the source on the detector. Restricting the analysis to a homogeneous subset of observations, with the source at the same detector position, we place strong limits on possible spectral or flux variations from March 2005 to present-day. A slightly higher temperature (kT~61.5 eV, compared to the average value kT~61 eV) was instead measured in April 2002. If this difference is not of instrumental origin, it implies a rate of variation of about 0.15 eV/yr between April 2002 and March 2005. The high-statistics spectrum from the selected observations is well fit by the sum of two blackbody models, which extrapolate to an optical flux level in agreement with the observed value.Comment: 4 pages, to appear in the proceedings of the ERPM conference, Zielona Gora, April 201

Preparation and Heavy Metal Ions Chelating Properties of Multifunctional Polymer-Grafted Silica Hybrid Materials

In this research work, novel hybrid materials based on multifunctional polymers and silica were developed and investigated in view of possible employment as sorbents for removal of heavy metal ions from water in presence of various ions. Organic-inorganic hybrid materials were prepared by covalent bonding of vinyl-terminated polyamidoamine (PAA) onto aminated silica particles. Two series of polyamidoamine-grafted silica, differing in the PAA chemical structure, were synthesized, and their heavy metal ions chelating properties were investigated. Column adsorption procedure for Cu, Zn, and Ni in aqueous solution was successfully established. Moreover, the adsorption behaviour of the materials was evaluated in different ionic strength solutions as well as in distilled and natural water. Organic-inorganic hybrid materials exhibited excellent chelating properties and selectivity for different metal ions. The hybrid columns showed exceptional eluting and regenerating property using diluted hydrochloric acid solution as eluent. In particular, the hybrid materials containing more carboxy groups possessed superior adsorption ability, reusability, and stability. The consecutive adsorption-desorption experiments exhibited that this material could be reused more than 20 cycles without almost any loss of adsorption capability. These new organic-inorganic sorbents appear very promising as an effective solid-phase extraction material for the selective preconcentration or removing of heavy metal ions from the environment