55 resultados para Residual autocorrelation and autocovariance matrices
Resumo:
Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.
Resumo:
The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.
Resumo:
Background: Many studies have illustrated that ambient air pollution negatively impacts on health. However, little evidence is available for the effects of air pollution on cardiovascular mortality (CVM) in Tianjin, China. Also, no study has examined which strata length for the time-stratified case–crossover analysis gives estimates that most closely match the estimates from time series analysis. Objectives: The purpose of this study was to estimate the effects of air pollutants on CVM in Tianjin, China, and compare time-stratified case–crossover and time series analyses. Method: A time-stratified case–crossover and generalized additive model (time series) were applied to examine the impact of air pollution on CVM from 2005 to 2007. Four time-stratified case–crossover analyses were used by varying the stratum length (Calendar month, 28, 21 or 14 days). Jackknifing was used to compare the methods. Residual analysis was used to check whether the models fitted well. Results: Both case–crossover and time series analyses show that air pollutants (PM10, SO2 and NO2) were positively associated with CVM. The estimates from the time-stratified case–crossover varied greatly with changing strata length. The estimates from the time series analyses varied slightly with changing degrees of freedom per year for time. The residuals from the time series analyses had less autocorrelation than those from the case–crossover analyses indicating a better fit. Conclusion: Air pollution was associated with an increased risk of CVM in Tianjin, China. Time series analyses performed better than the time-stratified case–crossover analyses in terms of residual checking.
Resumo:
Epithelial mesenchymal transition (EMT) and cancer stem cells (CSC) have been associated with resistance to chemotherapy. Eighty percent of ovarian cancer patients initially respond to platinum-based combination therapy but most return with recurrence and ultimate demise. To better understand such chemoresistance we have assessed the potential role of EMT in tumor cells collected from advanced-stage ovarian cancer patients and the ovarian cancer cell line OVCA 433 in response to cisplatin in vitro. We demonstrate that cisplatin-induced transition from epithelial to mesenchymal morphology in residual cancer cells correlated with reduced E-cadherin, and increased N-cadherin and vimentin expression. The mRNA expression of Snail, Slug, Twist, and MMP-2 were significantly enhanced in response to cisplatin and correlated with increased migration. This coincided with increased cell surface expression of CSC-like markers such as CD44, α2 integrin subunit, CD117, CD133, EpCAM, and the expression of stem cell factors Nanog and Oct-4. EMT and CSC-like changes in response to cisplatin correlated with enhanced activation of extracellular signal-regulated kinase (ERK)1/2. The selective MEK inhibitor U0126 inhibited ERK2 activation and partially suppressed cisplatin-induced EMT and CSC markers. In vivo xenotransplantation of cisplatin-treated OVCA 433 cells in zebrafish embryos demonstrated significantly enhanced migration of cells compared to control untreated cells. U0126 inhibited cisplatin-induced migration of cells in vivo, suggesting that ERK2 signaling is critical to cisplatin-induced EMT and CSC phenotypes, and that targeting ERK2 in the presence of cisplatin may reduce the burden of residual tumor, the ultimate cause of recurrence in ovarian cancer patients.
Resumo:
In transport networks, Origin-Destination matrices (ODM) are classically estimated from road traffic counts whereas recent technologies grant also access to sample car trajectories. One example is the deployment in cities of Bluetooth scanners that measure the trajectories of Bluetooth equipped cars. Exploiting such sample trajectory information, the classical ODM estimation problem is here extended into a link-dependent ODM (LODM) one. This much larger size estimation problem is formulated here in a variational form as an inverse problem. We develop a convex optimization resolution algorithm that incorporates network constraints. We study the result of the proposed algorithm on simulated network traffic.
Resumo:
Origin-Destination matrices (ODM) estimation can benefits of the availability of sample trajectories which can be measured thanks to recent technologies. This paper focus on the case of transport networks where traffic counts are measured by magnetic loops and sample trajectories available. An example of such network is the city of Brisbane, where Bluetooth detectors are now operating. This additional data source is used to extend the classical ODM estimation to a link-specific ODM (LODM) one using a convex optimisation resolution that incorporates networks constraints as well. The proposed algorithm is assessed on a simulated network.
Resumo:
Complementary experiments and numerical modeling reveal the important role of photo-ionization in the guided streamer propagation in helium-air gas mixtures. It is shown that the minimum electron concentration ∼108 cm−3 is required for the regular, repeated propagation of the plasma bullets, while the streamers propagate in the stochastic mode below this threshold. The stochastic-to-regular mode transition is related to the higher background electron density in front of the propagating streamers. These findings help improving control of guided streamer propagation in applications from health care to nanotechnology and improve understanding of generic pre-breakdown phenomena.
Resumo:
Bien Hoa Airbase was one of the bulk storage and supply facilities for defoliants during the Vietnam War. Environmental and biological samples taken around the airbase have elevated levels of dioxin. In 2007, a pre-intervention knowledge, attitude and practice (KAP) survey of local residents living in Trung Dung and Tan Phong wards was undertaken regarding appropriate strategies to reduce dioxin exposure. A risk reduction programme was implemented in 2008 and post-intervention KAP surveys were undertaken in 2009 and 2013 to evaluate the longer term impacts. Quantitative assessment was undertaken via a KAP survey in 2013 among 600 local residents randomly selected from the two intervention wards and one control ward (Buu Long). Eight in-depth interviews and two focus group discussions were also undertaken for qualitative assessment. Most programme activities had ceased and dioxin risk communication activities had not been integrated into local routine health education programmes; however, main results generally remained and were better than that in Buu Long. In total, 48.2% of households undertook measures to prevent exposure, higher than those in pre- and post-intervention surveys (25.8% and 39.7%) and the control ward (7.7%). Migration and the sensitive nature of dioxin issues were the main challenges for the programme's sustainability