Post traumatic success: Positive psychology and solution-focused strategies to help clients survive and thrive

I am an academic who has spent a career using a strengths-based approach in researching ways to promote and maintain mental health in people who have experienced trauma. When I read the title of the book, the notion of “post traumatic success” immediately brought many questions to my mind. What is success anyway? How do we measure success following trauma? Who decides if a person has been successful? However, as I started to read, the intention of the book became clear and my bias regarding the title lessened...

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

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.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

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.

Comparison of the binding stoichiometries of positively charged DNA-binding drugs using positive and negative ion electrospray ionization mass spectrometry

Positive and negative ion electrospray ionization (ESI) mass spectra of complexes of positively charged small molecules (distamycin, Hoechst 33258, [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2) have been compared. [Ru(phen)2dpq]Cl2 and [Ru(phen)2dpqC]Cl2 bind to DNA by intercalation. Negative ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA showed ions from DNA-ligand complexes consistent with solution studies. In contrast, only ions from freeDNAwere present in positive ion ESI mass spectra of mixtures of [Ru(phen)2dpq]Cl2 or [Ru(phen)2dpqC]Cl2 with DNA, highlighting the need for obtaining ESI mass spectra of non-covalent complexes under a range of experimental conditions. Negative ion spectra of mixtures of the minor groove binder Hoechst 33258 with DNA containing a known minor groove binding sequence were dominated by ions from a 1:1 complex. In contrast, in positive ion spectra there were also ions present from a 2:1 (Hoechst 33258: DNA) complex, suggesting an alternative binding mode was possible either in solution or in the gas phase. When Hoechst 33258 was mixed with a DNA sequence lacking a high affinity minor groove binding site, the negative ion ESI mass spectra showed that 1:1 and 2:1 complexes were formed, consistent with existence of binding modes other than minor groove binding. The data presented suggest that comparison of positive and negative ion ESI-MS spectra might provide an insight into various binding modes in both solution and the gas phase.

Study of the underlying electrochemistry of polycrystalline gold electrodes in aqueous solution and electrocatalysis by large amplitude Fourier transformed alternating current voltammetry

Polycrystalline gold electrodes of the kind that are routinely used in analysis and catalysis in aqueous media are often regarded as exhibiting relatively simple double-layer charging/discharging and monolayer oxide formation/ removal in the positive potential region. Application of the large amplitude Fourier transformed alternating current (FT-ac) voltammetric technique that allows the faradaic current contribution of fast electron-transfer processes to be emphasized in the higher harmonic components has revealed the presence of well-defined faradaic (premonolayer oxidation) processes at positive potentials in the double-layer region in acidic and basic media which are enhanced by electrochemical activation. These underlying quasi-reversible interfacial electron-transfer processes may mediate the course of electrocatalytic oxidation reactions of hydrazine, ethylene glycol, and glucose on gold electrodes in aqueous media. The observed responses support key assumptions associated with the incipient hydrous oxide adatom mediator (IHOAM) model of electrocatalysis.

Auto-inhibition of hydrogen gas evolution on gold in aqueous acid solution

It was demonstrated recently that dramatic changes in the redox behaviour of gold/aqueous solution interfaces may be observed following either cathodic or thermal electrode pretreatment. Further work on the cathodic pretreatment of gold in acid solution revealed that as the activity of the gold surface was increased, its performance as a substrate for hydrogen gas evolution under constant potential conditions deteriorated. The change in activity of the gold atoms at the interface, which was attributed to a hydrogen embrittlement process (the occurrence of the latter was subsequently checked by surface microscopy), was confirmed, as in earlier work, by the appearance of a substantial anodic peak at ca. 0.5 V (RHE) in a post-activation positive sweep. Changes in the catalytic activity of a metal surface reflect the fact that the structure (or topography), thermodynamic activity and electronic properties of a surface are dependent not only on pretreatment but also, in the case of the hydrogen evolution reaction, vary with time during the course of reaction. As will be reported shortly, similar (and often more dramatic) time-dependent behaviour was observed for hydrogen gas evolution on other metal electrodes.

Nutrition prescription to achieve positive outcomes in Chronic Kidney Disease : a systematic review

In Chronic Kidney Disease (CKD), management of diet is important in prevention of disease progression and symptom management, however evidence on nutrition prescription is limited. Recent international CKD guidelines and literature was reviewed to address the following question “What is the appropriate nutrition prescription to achieve positive outcomes in adult patients with chronic kidney disease?” Databases included in the search were Medline and CINAHL using EBSCOhost search engine, Embase and the Cochrane Database of Systematic Reviews published from 2000 to 2009. International guidelines pertaining to nutrition prescription in CKD were also reviewed from 2000 to 2013. Three hundred and eleven papers and eight guidelines were reviewed by three reviewers. Evidence was graded as per the National Health and Medical Research Council of Australia criteria. The evidence from thirty six papers was tabulated under the following headings: protein, weight loss, enteral support, vitamin D, sodium, fat, fibre, oral nutrition supplements, nutrition counselling, including protein and phosphate, nutrients in peritoneal dialysis solution and intradialytic parenteral nutrition, and was compared to international guidelines. While more evidence based studies are warranted, the customary nutrition prescription remains satisfactory with the exception of Vitamin D and phosphate. In these two areas, additional research is urgently needed given the potential of adverse outcomes for the CKD patient.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Random projections on manifolds of symmetric positive definite matrices for image classification

Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent spaces, or (2) embedding into Reproducing Kernel Hilbert Spaces (RKHS). While embedding into tangent spaces allows the use of existing Euclidean-based learning algorithms, manifold shape is only approximated which can cause loss of discriminatory information. The RKHS approach retains more of the manifold structure, but may require non-trivial effort to kernelise Euclidean-based learning algorithms. In contrast to the above approaches, in this paper we offer a novel solution that allows SPD matrices to be used with unmodified Euclidean-based learning algorithms, with the true manifold shape well-preserved. Specifically, we propose to project SPD matrices using a set of random projection hyperplanes over RKHS into a random projection space, which leads to representing each matrix as a vector of projection coefficients. Experiments on face recognition, person re-identification and texture classification show that the proposed approach outperforms several recent methods, such as Tensor Sparse Coding, Histogram Plus Epitome, Riemannian Locality Preserving Projection and Relational Divergence Classification.

Positive development and assessment

Purpose – There has been a tendency in sustainability science to be passive. The purpose of this paper is to introduce an alternative positive framework for a more active and direct approach to sustainable design and assessment that de-couples environmental impacts and economic growth. Design/methodology/approach – This paper deconstructs some systemic gaps that are critical to sustainability in built environment management processes and tools, and reframes negative “sustainable” decision making and assessment frameworks into their positive counterparts. In particular, it addresses the omission of ecology, design and ethics in development assessment. Findings – Development can be designed to provide ecological gains and surplus “eco-services,” but assessment tools and processes favor business-as-usual. Despite the tenacity of the dominant paradigm (DP) in sustainable development institutionalized by the Brundtland Report over 25 years ago, these omissions are easily corrected. Research limitations/implications – The limitation is that the author was unable to find exceptions to the omissions cited here in the extensive literature on urban planning and building assessment tools. However, exceptions prove the rule. The implication is that it is not too late for eco-positive retrofitting of cities to increase natural and social capital. The solutions are just as applicable in places like China and India as the USA, as they pay for themselves. Originality/value – Positive development (PD) is a fundamental paradigm shift that reverses the negative models, methods and metrics of the DP of sustainable development. This paper provides an example of how existing “negative” concepts and practices can be converted into positive ones through a PD prism. Through a new form of bio-physical design, development can be a sustainability solution.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.