Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

A Raman and infrared spectroscopic characterisation of the phosphate mineral phosphohedyphane Ca2Pb3(PO4)3Cl from the Roote mine, Nevada, USA

Phosphohedyphane Ca2Pb3(PO4)3Cl is rare Ca and Pb phosphate mineral that belongs to the apatite supergroup. We have analysed phosphohedyphane using SEM with EDX, and Raman and infrared spectroscopy. The chemical analysis shows the presence of Pb, Ca, P and Cl and the chemical formula is expressed as Ca2Pb3(PO4)3Cl. The very sharp Raman band at 975 cm−1 is assigned to the PO43-ν1 symmetric stretching mode. Raman bands noted at 1073, 1188 and 1226 cm−1 are to the attributed to the PO43-ν3 antisymmetric stretching modes. The two Raman bands at 835 and 812 cm−1 assigned to the AsO43-ν1 symmetric stretching vibration and AsO43-ν3 antisymmetric stretching modes prove the substitution of As for P in the structure of phosphohedyphane. A series of bands at 557, 577 and 595 cm−1 are attributed to the ν4 out of plane bending modes of the PO4 units. The multiplicity of bands in the ν2, ν3 and ν4 spectral regions provides evidence for the loss of symmetry of the phosphate anion in the phosphohedyphane structure. Observed bands were assigned to the stretching and bending vibrations of phosphate tetrahedra. Some Raman bands attributable to OH stretching bands were observed, indicating the presence of water and/or OH units in the structure.

Excitation of bound plasmons along nanoscale stripe waveguides: A comparison of end and grating coupling techniques

In this paper we excite bound long range stripe plasmon modes with a highly focused laser beam. We demonstrate highly confined plasmons propagating along a 50 μm long silver stripe 750 nm wide and 30 nm thick. Two excitation techniques were studied: focusing the laser spot onto the waveguide end and focusing the laser spot onto a silver grating. By comparing the intensity of the out-coupling photons at the end of the stripe for both grating and end excitation we are able to show that gratings provide an increase of a factor of two in the output intensity and thus out-coupling of plasmons excited by this technique are easier to detect. Authors expect that the outcome of this paper will prove beneficial for the development of passive nano-optical devices based on stripe waveguides, by providing insight into the different excitation techniques available and the advantages of each technique.

Integrated reporting and directors’ concerns about personal liability exposure: Law reform options

Integrated reporting () holds significant promise as a new reporting paradigm that is holistic, strategic, responsive, material, and relevant across multiple time frames. However, its uptake in Australia is being hampered by directors’ concerns about personal liability exposure, particularly for forward-looking statements that subsequently prove to be unfounded. This article seeks to illuminate the bases for these liability concerns by outlining the similarities between and the operating and financial review requirements under the Corporations Act 2001 (Cth), and the relevant grounds for liability for misleading and deceptive disclosures, and breach of directors’ duties. In light of this discussion, this article proposes four possible reform options, ranging from minor adaptations to the Framework to far-reaching reforms of the Corporations Act. As assurance is desirable to ensure that reliance can be placed on integrated reports, the development of a legal safe harbour for auditors of forward-looking information is also canvassed.

Using decision trees to understand structure in missing data

Objectives Demonstrate the application of decision trees – classification and regression trees (CARTs), and their cousins, boosted regression trees (BRTs) – to understand structure in missing data. Setting Data taken from employees at three different industry sites in Australia. Participants 7915 observations were included. Materials and Methods The approach was evaluated using an occupational health dataset comprising results of questionnaires, medical tests, and environmental monitoring. Statistical methods included standard statistical tests and the ‘rpart’ and ‘gbm’ packages for CART and BRT analyses, respectively, from the statistical software ‘R’. A simulation study was conducted to explore the capability of decision tree models in describing data with missingness artificially introduced. Results CART and BRT models were effective in highlighting a missingness structure in the data, related to the Type of data (medical or environmental), the site in which it was collected, the number of visits and the presence of extreme values. The simulation study revealed that CART models were able to identify variables and values responsible for inducing missingness. There was greater variation in variable importance for unstructured compared to structured missingness. Discussion Both CART and BRT models were effective in describing structural missingness in data. CART models may be preferred over BRT models for exploratory analysis of missing data, and selecting variables important for predicting missingness. BRT models can show how values of other variables influence missingness, which may prove useful for researchers. Conclusion Researchers are encouraged to use CART and BRT models to explore and understand missing data.

Start making sense: Applying a salutogenic model to architectural design for psychiatric care

Purpose This paper aims to look into the significance of architectural design in psychiatric care facilities. There is a strong correlation between perceptual dysfunction and psychiatric illness, and also between the patient and his environment. As such, even minor design choices can be of great consequence in a psychiatric facility. It is of critical importance, therefore, that a psychiatric milieu is sympathetic and does not exacerbate the psychosis. Design/methodology/approach This paper analyses the architectural elements that may influence mental health, using an architectural extrapolation of Antonovsky’s salutogenic theory, which states that better health results from a state of mind which has a fortified sense of coherence. According to the theory, a sense of coherence is fostered by a patient’s ability to comprehend the environment (comprehensibility), to be effective in his actions (manageability) and to find meaning (meaningfullness). Findings Salutogenic theory can be extrapolated in an architectural context to inform design choices when designing for a stress-sensitive client base. Research limitations/implications In the paper an architectural extrapolation of salutogenic theory is presented as a practical method for making design decisions (in praxis) when evidence is not available. As demonstrated, the results appear to reflect what evidence is available, but real evidence is always desirable over rationalist speculation. The method suggested here cannot prove the efficacy or appropriateness of design decisions and is not intended to do so. Practical implications The design of mental health facilities has long been dominated by unsubstantiated policy and normative opinions that do not always serve the client population. This method establishes a practical theoretical model for generating architectural design guidelines for mental health facilities. Originality/value The paper will prove to be helpful in several ways. First, salutogenic theory is a useful framework for improving health outcomes, but in the past the theory has never been applied in a methodological way. Second, there have been few insights into how the architecture itself can improve the functionality of a mental health facility other than improve the secondary functions of hospital services.

Evaluation of a patient-specific finite-element model to simulate conservative treatment in adolescent idiopathic scoliosis

Study design Retrospective validation study. Objectives To propose a method to evaluate, from a clinical standpoint, the ability of a finite-element model (FEM) of the trunk to simulate orthotic correction of spinal deformity and to apply it to validate a previously described FEM. Summary of background data Several FEMs of the scoliotic spine have been described in the literature. These models can prove useful in understanding the mechanisms of scoliosis progression and in optimizing its treatment, but their validation has often been lacking or incomplete. Methods Three-dimensional (3D) geometries of 10 patients before and during conservative treatment were reconstructed from biplanar radiographs. The effect of bracing was simulated by modeling displacements induced by the brace pads. Simulated clinical indices (Cobb angle, T1–T12 and T4–T12 kyphosis, L1–L5 lordosis, apical vertebral rotation, torsion, rib hump) and vertebral orientations and positions were compared to those measured in the patients' 3D geometries. Results Errors in clinical indices were of the same order of magnitude as the uncertainties due to 3D reconstruction; for instance, Cobb angle was simulated with a root mean square error of 5.7°, and rib hump error was 5.6°. Vertebral orientation was simulated with a root mean square error of 4.8° and vertebral position with an error of 2.5 mm. Conclusions The methodology proposed here allowed in-depth evaluation of subject-specific simulations, confirming that FEMs of the trunk have the potential to accurately simulate brace action. These promising results provide a basis for ongoing 3D model development, toward the design of more efficient orthoses.

Risk factors for hospital re-presentation among older adults following fragility fractures: Protocol for a systematic review

Background After being discharged from hospital following the acute management of a fragility fracture, older adults may re-present to hospital emergency departments in the post-discharge period. Early re-presentation to hospital, which includes hospital readmissions, and emergency department presentations without admission, may be considered undesirable for individuals, hospital institutions and society. The identification of modifiable risk factors for hospital re-representation following initial fracture management may prove useful for informing policy or practice initiatives that seek to minimise the need for older adults to re-present to hospital early after they have been discharged from their initial inpatient care. The purpose of this systematic review is to identify correlates of hospital re-presentation in older patients who have been discharged from hospital following clinical management of fragility fractures. Methods/Design The review will follow the PRISMA-P reporting guidelines for systematic reviews. Four electronic databases (Pubmed, CINAHL, Embase, and Scopus) will be searched. A suite of search terms will identify peer-reviewed articles that have examined the correlates of hospital re-presentation in older adults (mean age of 65 years or older) who have been discharged from hospital following treatment for fragility fractures. The Effective Public Health Practice Project Quality Assessment Tool for Quantitative Studies will be used to assess the quality of the studies. The strength of evidence will be assessed through best evidence synthesis. Clinical and methodological heterogeneity across studies are likely to impede meta-analyses. Discussion The best evidence synthesis will outline correlates of hospital re-presentations in this clinical group. This synthesis will take into account potential risks of bias for each study, while permitting inclusion of findings from a range of quantitative study designs. It is anticipated that findings from the review will be useful in identifying potentially modifiable risk factors that have relevance in policy, practice and research priorities to improve the management of patients with fragility fractures. Systematic Review Registration PROSPERO CRD42015019379

fMRI evidence of word frequency and strength effects during episodic memory encoding

Word frequency (WF) and strength effects are two important phenomena associated with episodic memory. The former refers to the superior hit-rate (HR) for low (LF) compared to high frequency (HF) words in recognition memory, while the latter describes the incremental effect(s) upon HRs associated with repeating an item at study. Using the "subsequent memory" method with event-related fMRI, we tested the attention-at-encoding (AE) [M. Glanzer, J.K. Adams, The mirror effect in recognition memory: data and theory, J. Exp. Psychol.: Learn Mem. Cogn. 16 (1990) 5-16] explanation of the WF effect. In addition to investigating encoding strength, we addressed if study involves accessing prior representations of repeated items via the same mechanism as that at test [J.L. McClelland, M. Chappell, Familiarity breeds differentiation: a subjective-likelihood approach to the effects of experience in recognition memory, Psychol. Rev. 105 (1998) 724-760], entailing recollection [K.J. Malmberg, J.E. Holden, R.M. Shiffrin, Modeling the effects of repetitions, similarity, and normative word frequency on judgments of frequency and recognition memory, J. Exp. Psychol.: Learn Mem. Cogn. 30 (2004) 319-331] and whether less processing effort is entailed for encoding each repetition [M. Cary, L.M. Reder, A dual-process account of the list-length and strength-based mirror effects in recognition, J. Mem. Lang. 49 (2003) 231-248]. The increased BOLD responses observed in the left inferior prefrontal cortex (LIPC) for the WF effect provide support for an AE account. Less effort does appear to be required for encoding each repetition of an item, as reduced BOLD responses were observed in the LIPC and left lateral temporal cortex; both regions demonstrated increased responses in the conventional subsequent memory analysis. At test, a left lateral parietal BOLD response was observed for studied versus unstudied items, while only medial parietal activity was observed for repeated items at study, indicating that accessing prior representations at encoding does not necessarily occur via the same mechanism as that at test, and is unlikely to involve a conscious recall-like process such as recollection. This information may prove useful for constraining cognitive theories of episodic memory.

The semantic interference effect in the picture-word paradigm: An event-related fMRI study employing overt responses

We used event-related functional magnetic resonance imaging (fMRI) to investigate neural responses associated with the semantic interference (SI) effect in the picture-word task. Independent stage models of word production assume that the locus of the SI effect is at the conceptual processing level (Levelt et al. [1999]: Behav Brain Sci 22:1-75), whereas interactive models postulate that it occurs at phonological retrieval (Starreveld and La Heij [1996]: J Exp Psychol Learn Mem Cogn 22:896-918). In both types of model resolution of the SI effect occurs as a result of competitive, spreading activation without the involvement of inhibitory links. These assumptions were tested by randomly presenting participants with trials from semantically-related and lexical control distractor conditions and acquiring image volumes coincident with the estimated peak hemodynamic response for each trial. Overt vocalization of picture names occurred in the absence of scanner noise, allowing reaction time (RT) data to be collected. Analysis of the RT data confirmed the SI effect. Regions showing differential hemodynamic responses during the SI effect included the left mid section of the middle temporal gyrus, left posterior superior temporal gyrus, left anterior cingulate cortex, and bilateral orbitomedial prefrontal cortex. Additional responses were observed in the frontal eye fields, left inferior parietal lobule, and right anterior temporal and occipital cortex. The results are interpreted as indirectly supporting interactive models that allow spreading activation between both conceptual processing and phonological retrieval levels of word production. In addition, the data confirm that selective attention/response suppression has a role in resolving the SI effect similar to the way in which Stroop interference is resolved. We conclude that neuroimaging studies can provide information about the neuroanatomical organization of the lexical system that may prove useful for constraining theoretical models of word production.

Mauve: How one man invented the colour that changed the world

In an essay, "The Books of Last Things", Delia Falconer discusses the emergence of a new genre in publishing - microhistories. She cites a number of recent titles in non-fiction and fiction - Longitude, Cod, Tulips, Pushkin's Button, Nathaniel's Nutmeg, Zarafa, The Surgeon of Crowthorne, The Potato, The Perfect Storm. Delia Falconer observes of this tradition: "One has the sense, reading these books, of a surprising weight, of pleasant shock. In part, it is because we are looking at things which are generally present around us, but modestly out of sight and mind - historical nitty gritty like cod, potatoes, longitudinal clocks - which the authors have thrust suddenly, like a Biblical visitation of frogs or locusts, in our face. Things like spice and buttons and clocks are generally seen to enable history on the large scale, but are not often viewed as its worthy subjects. And by the same grand logic of history, more unusual phenomena like cabinets of curiosities or glass-making or farm lore or sailors' knots are simply odd blips on its radar screen, interesting footnotes. These new books, microhistories, reverse the usual order of history, which argues from the general to the particular, in order to prove its inevitable progress. They start from the footnotes. But by reversing the process, and walking through the back door of history, you don't necessarily end up at the front of the same house." Delia Falconer speculates about the reasons for the popularity of microhistories. She concludes: "I would like to think that reading them is not simply an exercise in nostalgia, but a challenge to the present". In Mauve, Simon Garfield provides a new way of thinking and writing about the history of intellectual property. Instead of providing a grand historical narrative of intellectual property, he tells the story of a particular invention, and its exploitation. Simon Garfield relates how English chemist William Perkin accidentally discovered a way to mass-produce colour mauve in a factory. Working on a treatment for malaria in his London home laboratory, Perkin failed to produce artificial quinine. Instead he created a dark oily sludge that turned silk a beautiful light purple. The colour was unique and became the most desirable shade in the fashion houses of Paris and London. ... The book Mauve will have a number of contemporary resonances for intellectual property lawyers and academics. Simon Garfield emphasizes the difficulties inherent in commercialising an invention and managing intellectual property. He investigates the uneasy collaboration between industry and science. Simon Garfield suggests that complaints about the efficacy of patent offices are perennial. He also highlights the problems faced by courts and law-makers in accommodating new technologies within the logic of patent law. In his elegant microhistory of the colour mauve, Simon Garfield confirms the conclusion of Brad Sherman and Lionel Bently that many aspects of modern intellectual property law can only be understood through an understanding of the past: "The image of intellectual property law that developed during the 19th century and the narrative of identity which this engendered played and continue to play an important role in the way we think about and understand intellectual property law".

Matters Arising: Role of HLA genes in familial spondyloarthropathy

Said-Nahal and colleagues report an intriguing finding of an association with HLA-DR4 independent of B27 in families with ankylosing spondylitis (AS),1 a finding highlighted by an accompanying editorial.2 The approach of studying B27 positive and B27 negative haplotypes may prove powerful in identifying further cis or trans encoded genes involved in AS. However, the reported association of DR4 with AS is quite a surprising finding given that no difference was noted in B27-DR4 haplotype frequencies in patients and ethnically matched healthy controls. Many previous studies have not reported any such association,3–9 including a similar preliminary study by the same authors.10 Although these studies were mainly case-control studies, population stratification is highly unlikely to cause a false negative finding if the effect size of the reported association with DR4 is as high as Said-Nahal and colleagues describe...

Introduction: Epitope mimicry as a component cause of autoimmune disease

The causes of autoimmune diseases have yet to be fully elucidated. Autoantibodies, autoreactive T cell responses, the presence of a predisposing major histocompatibility complex (MHC) haplotype and responsiveness to corticosteroids are features, and some are possibly contributory causes of autoimmune disease. The most challenging question is how autoimmune diseases are triggered. Molecular mimicry of host cell determinants by epitopes of infectious agents with ensuing cross-reactivity is one of the most popular yet still controversial theories for the initiation of autoimmune diseases [1]. Throughout the 1990s, hundreds of research articles focusing to various extents on epitope mimicry, as it is more accurately described in an immunological context, were published annually. Many of these articles presented data that were consistent with the hypothesis of mimicry but that did not actually prove the theory. Other equally convincing reports indicated that epitope mimicry was not the cause of the autoimmune disease despite sequence similarity between molecules of infectious agents and the host. Some 20 years ago, Rothman [2] proposed a model for disease causation and I have used this as a framework to examine the role of epitope mimicry in the development of autoimmune disease. The thesis of Rothman’s model is that an effect, in this instance autoimmune disease, arises as a result of a cause. In most cases, multiple-component causes contribute synergistically to yield the effect, and each of these components alone is insufficient as a cause. Logically, some component causes, such as the presence of a particular autoimmune response, are also necessary causes.