869 resultados para Almost Sure Convergence
Resumo:
Assessed correlates of alcohol consumption (AC) in 212 undergraduates (81 "college" and 131 "noncollege" residents [COLRs and NCOLRs], mean ages 18.9 and 18.6 yrs, respectively) and studied the proportion who were drinking at potentially harmful levels (HLs). This study also examined changes in AC during the course of the 1st semester and predicted drinking levels in the 2nd semester from demographics, drug use, social variables and self-efficacy data. Data were collected using self-administered questionnaires. During both semesters, the COLRs reported drinking significantly more alcohol than NCOLRs, but during vacation the intake of the 2 groups was almost equal. Higher AC in the 2nd semester was best predicted by higher AC during the 1st semester, followed by more AC by friends and higher parental occupation status. Female COLRs were those most likely to be drinking at HLs. Results also showed that a significant proportion of COLRs were drinking at HLs.
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There has been an extended engagement with how young people experience policing, with a focus on the intersection between policing and indigeneity, ethnicity, gender, and social class. Interestingly, sexuality and/or gender diversity has been almost completely overlooked, both nationally and internationally. This paper reports on LGBT youth service providers’ accounts about police and LGBT young people interactions. It overviews the outcomes of semi-structured interviews with key LGBT youth service providers in different regions of Brisbane, Queensland. As the first qualitative engagement with these issues from the perspective of service providers, it highlights not only how LGBT young people experience policing, but also how service providers need to ‘work the system’ of policing to produce the best outcomes for LGBT young people.
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This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.
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Literature on Ubiquitous Eco Cities highlights three key issues to be carefully considered while planning, developing and managing such cities: ‘technology, infrastructure and management’. This paper discusses the recent developments in telecommunication networks, trends in technology convergence and both of their implications on the management of Ubiquitous Eco Cities. The paper also introduces recent approaches on urban management, such as intelligent urban management systems, that are potentially suitable for Ubiquitous Eco Cities.
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OBJECTIVES: To quantify the driving difficulties of older adults using a detailed assessment of driving performance and to link this with self-reported retrospective and prospective crashes. DESIGN: Prospective cohort study. SETTING: On-road driving assessment. PARTICIPANTS: Two hundred sixty-seven community-living adults aged 70 to 88 randomly recruited through the electoral roll. MEASUREMENTS: Performance on a standardized measure of driving performance. RESULTS: Lane positioning, approach, and blind spot monitoring were the most common error types, and errors occurred most frequently in situations involving merging and maneuvering. Drivers reporting more retrospective or prospective crashes made significantly more driving errors. Driver instructor interventions during self-navigation (where the instructor had to brake or take control of the steering to avoid an accident) were significantly associated with higher retrospective and prospective crashes; every instructor intervention almost doubled prospective crash risk. CONCLUSION: These findings suggest that on-road driving assessment provides useful information on older driver difficulties, with the self-directed component providing the most valuable information.
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Thousands of Australian children are sexually abused every year, and the effects can be severe and long lasting. Not only is child sexual abuse a public health problem, but the acts inflicted are criminal offences. Child sexual abuse usually occurs in private, typically involving relationships featuring a massive imbalance in power and an abuse of that power. Those who inflict child sexual abuse seek to keep it secret, whether by threats or more subtle persuasion. As a method of responding to this phenomenon and in an effort to uncover cases of sexual abuse that otherwise would not come to light, governments in Australian States and Territories have enacted legislation requiring designated persons to report suspected child sexual abuse. With Western Australia’s new legislation having commenced on 1 January 2009, every Australian State and Territory government has now passed these laws, so that there is now, for the first time, an almost harmonious legislative approach across Australia to the reporting of child sexual abuse. Yet there remain differences in the State and Territory laws regarding who has to make reports, which cases of sexual abuse are required to be reported, and whether suspected future abuse must be reported. These differences indicate that further refinement of the laws is required
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Background: The incidence of obesity is increasing; this is of major concern, as obesity is associated with cardiovascular disease, stroke, type 2 diabetes, respiratory tract disease, and cancer. Objectives/methods: This evaluation is of a Phase II clinical trial with tesofensine in obese subjects. Results: After 26 weeks, tesofensine caused a significant weight loss, and may have a higher maximal ability to reduce weight than the presently available anti-obesity agents. However, tesofensine also increased blood pressure and heart rate, and may increase psychiatric disorders. Conclusions: It is encouraging that tesofensine 0.5 mg may cause almost double the weight loss observed with sibutramine or rimonabant. As tesofensine and sibutramine have similar pharmacological profiles, it would be of interest to compare the weight loss with tesofensine in a head-to-head clinical trial with sibutramine, to properly assess their comparative potency. Also, as teso fensine 0.5 mg increases heart rate, as well as increasing the incidence of adverse effects such as nausea, drug mouth, flatulence, insomnia, and depressed mode, its tolerability needs to be further evaluated in large Phase III clinical trials.
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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.
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In what follows, I put forward an argument for an analytical method for social science that operates at the level of genre. I argue that generic convergence, generic hybridity, and generic instability provide us with a powerful perspectives on changes in political, cultural, and economic relationships, most specifically at the level of institutions. Such a perspective can help us identify the transitional elements, relationships, and trajectories that define the place of our current system in history, thereby grounding our understanding of possible futures.1 In historically contextualising our present with this method, my concern is to indicate possibilities for the future. Systemic contradictions indicate possibility spaces within which systemic change must and will emerge. We live in a system currently dominated by many fully-expressed contradictions, and so in the presence of many possible futures. The contradictions of the current age are expressed most overtly in the public genres of power politics. Contemporary public policy—indeed politics in general-is an excellent focus for any investigation of possible futures, precisely because of its future-oriented function. It is overtly hortatory; it is designed ‘to get people to do things’ (Muntigl in press: 147). There is no point in trying to get people to do things in the past. Consequently, policy discourse is inherently oriented towards creating some future state of affairs (Graham in press), along with concomitant ways of being, knowing, representing, and acting (Fairclough 2000).
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In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis
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In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
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Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.
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In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.
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In this paper, a two-dimensional non-continuous seepage flow with fractional derivatives (2D-NCSF-FD) in uniform media is considered, which has modified the well known Darcy law. Using the relationship between Riemann-Liouville and Grunwald-Letnikov fractional derivatives, two modified alternating direction methods: a modified alternating direction implicit Euler method and a modified Peaceman-Rachford method, are proposed for solving the 2D-NCSF-FD in uniform media. The stability and consistency, thus convergence of the two methods in a bounded domain are discussed. Finally, numerical results are given.
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In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.