Diffusion indices on magnetic resonance imaging and neuropsychological performance in amnestic mild cognitive impairment

Background: Magnetic resonance diffusion tensor imaging (DTI) shows promise in the early detection of microstructural pathophysiological changes in the brain. Objectives: To measure microstructural differences in the brains of participants with amnestic mild cognitive impairment (MCI) compared with an age-matched control group using an optimised DTI technique with fully automated image analysis tools and to investigate the correlation between diffusivity measurements and neuropsychological performance scores across groups. Methods: 34 participants (17 participants with MCI, 17 healthy elderly adults) underwent magnetic resonance imaging (MRI)-based DTI. To control for the effects of anatomical variation, diffusion images of all participants were registered to standard anatomical space. Significant statistical differences in diffusivity measurements between the two groups were determined on a pixel-by-pixel basis using gaussian random field theory. Results: Significantly raised mean diffusivity measurements (p<0.001) were observed in the left and right entorhinal cortices (BA28), posterior occipital-parietal cortex (BA18 and BA19), right parietal supramarginal gyrus (BA40) and right frontal precentral gyri (BA4 and BA6) in participants with MCI. With respect to fractional anisotropy, participants with MCI had significantly reduced measurements (p<0.001) in the limbic parahippocampal subgyral white matter, right thalamus and left posterior cingulate. Pearson's correlation coefficients calculated across all participants showed significant correlations between neuropsychological assessment scores and regional measurements of mean diffusivity and fractional anisotropy. Conclusions: DTI-based diffusivity measures may offer a sensitive method of detecting subtle microstructural brain changes associated with preclinical Alzheimer's disease.

Visualization tools for high angular resolution diffusion imaging

There is a major effort in medical imaging to develop algorithms to extract information from DTI and HARDI, which provide detailed information on brain integrity and connectivity. As the images have recently advanced to provide extraordinarily high angular resolution and spatial detail, including an entire manifold of information at each point in the 3D images, there has been no readily available means to view the results. This impedes developments in HARDI research, which need some method to check the plausibility and validity of image processing operations on HARDI data or to appreciate data features or invariants that might serve as a basis for new directions in image segmentation, registration, and statistics. We present a set of tools to provide interactive display of HARDI data, including both a local rendering application and an off-screen renderer that works with a web-based viewer. Visualizations are presented after registration and averaging of HARDI data from 90 human subjects, revealing important details for which there would be no direct way to appreciate using conventional display of scalar images.

Investigating brain connectivity heritability in a twin study using diffusion imaging data

Heritability of brain anatomical connectivity has been studied with diffusion-weighted imaging (DWI) mainly by modeling each voxel's diffusion pattern as a tensor (e.g., to compute fractional anisotropy), but this method cannot accurately represent the many crossing connections present in the brain. We hypothesized that different brain networks (i.e., their component fibers) might have different heritability and we investigated brain connectivity using High Angular Resolution Diffusion Imaging (HARDI) in a cohort of twins comprising 328 subjects that included 70 pairs of monozygotic and 91 pairs of dizygotic twins. Water diffusion was modeled in each voxel with a Fiber Orientation Distribution (FOD) function to study heritability for multiple fiber orientations in each voxel. Precision was estimated in a test-retest experiment on a sub-cohort of 39 subjects. This was taken into account when computing heritability of FOD peaks using an ACE model on the monozygotic and dizygotic twins. Our results confirmed the overall heritability of the major white matter tracts but also identified differences in heritability between connectivity networks. Inter-hemispheric connections tended to be more heritable than intra-hemispheric and cortico-spinal connections. The highly heritable tracts were found to connect particular cortical regions, such as medial frontal cortices, postcentral, paracentral gyri, and the right hippocampus.

How does angular resolution affect diffusion imaging measures?

A key question in diffusion imaging is how many diffusion-weighted images suffice to provide adequate signal-to-noise ratio (SNR) for studies of fiber integrity. Motion, physiological effects, and scan duration all affect the achievable SNR in real brain images, making theoretical studies and simulations only partially useful. We therefore scanned 50 healthy adults with 105-gradient high-angular resolution diffusion imaging (HARDI) at 4T. From gradient image subsets of varying size (6 ≤ N ≤ 94) that optimized a spherical angular distribution energy, we created SNR plots (versus gradient numbers) for seven common diffusion anisotropy indices: fractional and relative anisotropy (FA, RA), mean diffusivity (MD), volume ratio (VR), geodesic anisotropy (GA), its hyperbolic tangent (tGA), and generalized fractional anisotropy (GFA). SNR, defined in a region of interest in the corpus callosum, was near-maximal with 58, 66, and 62 gradients for MD, FA, and RA, respectively, and with about 55 gradients for GA and tGA. For VR and GFA, SNR increased rapidly with more gradients. SNR was optimized when the ratio of diffusion-sensitized to non-sensitized images was 9.13 for GA and tGA, 10.57 for FA, 9.17 for RA, and 26 for MD and VR. In orientation density functions modeling the HARDI signal as a continuous mixture of tensors, the diffusion profile reconstruction accuracy rose rapidly with additional gradients. These plots may help in making trade-off decisions when designing diffusion imaging protocols.

Analyzing multi-fiber reconstruction in high angular resolution diffusion imaging using the tensor distribution function

High-angular resolution diffusion imaging (HARDI) can reconstruct fiber pathways in the brain with extraordinary detail, identifying anatomical features and connections not seen with conventional MRI. HARDI overcomes several limitations of standard diffusion tensor imaging, which fails to model diffusion correctly in regions where fibers cross or mix. As HARDI can accurately resolve sharp signal peaks in angular space where fibers cross, we studied how many gradients are required in practice to compute accurate orientation density functions, to better understand the tradeoff between longer scanning times and more angular precision. We computed orientation density functions analytically from tensor distribution functions (TDFs) which model the HARDI signal at each point as a unit-mass probability density on the 6D manifold of symmetric positive definite tensors. In simulated two-fiber systems with varying Rician noise, we assessed how many diffusionsensitized gradients were sufficient to (1) accurately resolve the diffusion profile, and (2) measure the exponential isotropy (EI), a TDF-derived measure of fiber integrity that exploits the full multidirectional HARDI signal. At lower SNR, the reconstruction accuracy, measured using the Kullback-Leibler divergence, rapidly increased with additional gradients, and EI estimation accuracy plateaued at around 70 gradients.

Innovation in Road Building: Removing Obstacles for Diffusion of Novel Building Products

How can obstacles to innovation be overcome in road construction? Using a focus group methodology, and based on two prior rounds of empirical work, the analysis in this chapter generates a set of four key solutions to two main construction innovation obstacles: (1) restrictive tender assessment and (2) disagreement over who carries the risk of new product failure. The four key solutions uncovered were: 1) pre-project product certification; 2) past innovation performance assessment; 3) earlier involvement of product suppliers and road asset operators; and 4) performance-based specifications. Additional research is suggested in order to illicit deeper insights into possible solutions to construction innovation obstacles, and should emphasise furthering the theoretical interpretation of empirical phenomena.

‘Just choose the easy option’: Students talk about alcohol use and social influence

Previous research into young people’s drinking behaviour has studied how social practices influence their actions and how they negotiate drinking-related identities. Here, adopting the perspective of discursive psychology we examine how, for young people, social influences are bound up with issues of drinking and of identity. We conducted 19 focus groups with undergraduate students in Australia aged between 18 and 24 years. Thematic analysis of participants’ accounts for why they drink or do not drink was used to identify passages of talk that referred to social influence, paying particular attention to terms such as ‘pressure’ and ‘choice’. These passages were then analysed in fine-grained detail, using discourse analysis, to study how participants accounted for social influence. Participants treated their behaviour as accountable and produced three forms of account that: (1) minimised the choice available to them, (2) explained drinking as culture and (3) described resisting peer pressure. They also negotiated gendered social dynamics related to drinking. These forms of account allowed the participants to avoid individual responsibility for drinking or not drinking. These findings demonstrate that the effects of social influence on young people’s drinking behaviour cannot be assumed, as social influence itself becomes negotiable within local contexts of talk about drinking.

IT pricing: Copyright law, consumer rights, and competition policy. A submission to the House of Representatives Standing Committee on Infrastructure and Communications Inquiry into IT Pricing

For a hundred years, since Federation, Australian consumers have suffered the indignity and the tragedy of price discrimination. From the time of imperial publishing networks, Australia has been suffered from cultural colonialism. In respect of pricing of copyright works, Australian consumers have been gouged; ripped-off; and exploited. Digital technologies have not necessarily brought an end to such price discrimination. Australian consumers have been locked out by technological protection measures; subject to surveillance, privacy intrusions and security breaches; locked into walled gardens by digital rights management systems; and geo-blocked.

The case for unitary taxation with formulary apportionment in the finance sector and the effect on developing nations

In 2013 the OECD released its 15 point Action plan to deal with base erosion and profit shifting (BEPS). In that plan it was recognised that BEPS has a significant effect on developing countries. This is because the lack of tax revenue can lead to a critical underfunding of public investment that would help promote economic growth. To this end, the BEPS project is aimed at ensuring an inclusive approach to take into account not only views of the G20 and OECD countries but also the perspective of developing nations. With this focus in mind and in the context of developing nations, the purpose of this article is to consider a possible solution to profit shifting which occurs under the current transfer pricing regime, with that solution being unitary taxation with formulary apportionment. It does so using the finance sector as a specific case for application. Multinational financial institutions (MNFIs) play a significant role in financing activities of their clients in developing nations. Consistent with the ‘follow-the-client’ phenomenon which explains financial institution expansion, these entities are increasingly profiting from activities associated with this growing market. Further, not only are MNFIs persistent users of tax havens but also, more than other industries, have opportunities to reduce tax through transfer pricing measures. This article establishes a case for an industry specific adoption of unitary taxation with formulary apportionment as a viable alternative to the current regime. It argues that such a model would benefit not only developed nations but also developing nations which are currently suffering the effects of BEPS. In doing so, it considers the practicalities of such an implementation by examining both definitional issues and a possible formula for MNFIs. This article argues that, while there would be implementation difficulties to overcome, the current domestic models of formulary apportionment provide important guidance as to how the unitary business and business activities of MNFIs should be defined as well as factors that should be included in an allocation formula, along with the appropriate weighting. While it would be difficult for developing nations to adopt such a regime, it is argued that it would be no more difficult than addressing issues they face with the current transfer pricing regime. As such, this article concludes that unitary taxation with formulary apportionment is a viable industry specific alternative for MNFIs which would assist developing nations and aid independent fiscal soundness.

Unitary Taxation of the Finance Sector

Multinational financial institutions (MNFIs) play a significant role in financing the activities of their clients in developing nations. Consistent with the ‘follow-the-customer’ phenomenon which explains financial institution expansion, these entities are increasingly profiting from activities associated with this growing market. However, not only are MNFIs persistent users of tax havens, but also, more than other industries, have the opportunity to reduce tax through transfer pricing measures. This paper establishes a case for an industry-specific adoption of unitary taxation with formulary apportionment as a viable alternative to the current regime. In doing so, it considers the practicalities of implementing this by examining both definitional issues and possible formulas for MNFIs. This paper argues that, while there would be implementation difficulties to overcome, the current domestic models of formulary apportionment provide important guidance as to how the unitary business and business activities of MNFIs should be defined, as well as the factors that should be included in an allocation formula, and the appropriate weighting. This paper concludes that unitary taxation with formulary apportionment is a viable industry-specific alternative for MNFIs.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Breaches of lease between exercise of option to renew and expiry of lease in Queensland

The decision of Greppo v Jam-Cal Bundaberg Pty Ltd [2015] QCA 131 illustrates a defect in s 128 of the Property Law Act 1974(Qld) which gives a right to a lessee to apply for relief against forfeiture against loss of a right to exercise an option to renew. The defect arises because the legislation does not adequately deal with breaches that occur after the exercise of the option but before the expiry of the lease. Most commercial leases of all kinds have a standard provisions, as the lease in this case, as a conditions of the exercise of the option to renew that the lessee will have given notice of exercise within the time specified to the lessor and will have up to the date of expiry of the lease paid all rent and observed all lessee’s covenants. The difficulties occur because invariably an option must be exercised before the expiry of the lease when a lessee may not be in breach of the lease but may later prior to the expiry of the lease fall into breach. As this decision indicates,at least in Queensland, that the lessee who desires to challenge the lessor’s right to enforce those conditions can neither seek relief under s 128 against forfeiture of the right to exercise the option ,or indeed, under s 124 of the Property Law Act 1974 to preserve the agreement for lease brought about by the otherwise regular exercise of the option to renew. The decision cries out for legislative reform along the lines of s 133E of the Conveyancing Act 1919(NSW) which was amended in 2001 to meet this contingency.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Fractional diffusion models of cardiac electrical propagation: Role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

A directed continuous time random walk model with jump length depending on waiting time

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x,t) of finding the walker at position at time is completely determined by the Laplace transform of the probability density function φ(t) of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.