Standardising corneal nerve fibre length for nerve tortuosity increases its association with measures of diabetic neuropathy

AIMS: Recent studies on corneal markers have advocated corneal nerve fibre length as the most important measure of diabetic peripheral neuropathy. The aim of this study was to determine if standardizing corneal nerve fibre length for tortuosity increases its association with other measures of diabetic peripheral neuropathy. METHODS: Two hundred and thirty-one individuals with diabetes with either predominantly mild or absent neuropathic changes and 61 control subjects underwent evaluation of diabetic neuropathy symptom score, neuropathy disability score, testing with 10-g monofilament, quantitative sensory testing (warm, cold, vibration detection) and nerve conduction studies. Corneal nerve fibre length and corneal nerve fibre tortuosity were measured using corneal confocal microscopy. A tortuosity-standardised corneal nerve fibre length variable was generated by dividing corneal nerve fibre length by corneal nerve fibre tortuosity. Differences in corneal nerve morphology between individuals with and without diabetic peripheral neuropathy and control subjects were determined and associations were estimated between corneal morphology and established tests of, and risk factors for, diabetic peripheral neuropathy. RESULTS: The tortuosity-standardised corneal nerve fibre length variable was better than corneal nerve fibre length in demonstrating differences between individuals with diabetes, with and without neuropathy (tortuosity-standardised corneal nerve fibre length variable: 70.5 ± 27.3 vs. 84.9 ± 28.7, P < 0.001, receiver operating characteristic area under the curve = 0.67; corneal nerve fibre length: 15.9 ± 6.9 vs. 18.4 ± 6.2 mm/mm(2) , P = 0.004, receiver operating characteristic area under the curve = 0.64). Furthermore, the tortuosity-standardised corneal nerve fibre length variable demonstrated a significant difference between the control subjects and individuals with diabetes, without neuropathy, while corneal nerve fibre length did not (tortuosity-standardised corneal nerve fibre length variable: 94.3 ± 27.1 vs. 84.9 ± 28.7, P = 0.028; corneal nerve fibre length: 20.1 ± 6.3 vs. 18.4 ± 6.2 mm/mm(2) , P = 0.084). Correlations between corneal nerve fibre length and established measures of neuropathy and risk factors for neuropathy were higher when a correction was made for the nerve tortuosity. CONCLUSIONS: Standardizing corneal nerve fibre length for tortuosity enhances the ability to differentiate individuals with diabetes, with and without neuropathy.

Arm’s length pricing and multinational banks : an old fashioned approach in a modern world

In “Arm’s Length Pricing and Multinational Banks: An Old Fashioned Approach in a Modern World”, Kerrie Sadiq, describes the high level of integration of multinational financial institutions and argues that treating each element within a given operation as a separate entity for transfer pricing purposes is not economically or legally realistic. She proposes instead formulary apportionment as a device for managing this complexity.

Transfer pricing and multinational financial institutions : the case for replacing arm’s length price with a unitary approach

The international tax system, designed a century ago, has not kept pace with the modern multinational entity rendering it ineffective in taxing many modern businesses according to economic activity. One of those modern multinational entities is the multinational financial institution (MNFI). The recent global financial crisis provides a particularly relevant and significant example of the failure of the current system on a global scale. The modern MNFI is increasingly undertaking more globalised and complex trading operations. A primary reason for the globalisation of financial institutions is that they typically ‘follow-the-customer’ into jurisdictions where international capital and international investors are required. The International Monetary Fund (IMF) recently reported that from 1995-2009, foreign bank presence in developing countries grew by 122 per cent. The same study indicates that foreign banks have a 20 per cent market share in OECD countries and 50 per cent in emerging markets and developing countries. Hence, most significant is that fact that MNFIs are increasingly undertaking an intermediary role in developing economies where they are financing core business activities such as mining and tourism. IMF analysis also suggests that in the future, foreign bank expansion will be greatest in emerging economies. The difficulties for developing countries in applying current international tax rules, especially the current traditional transfer pricing regime, are particularly acute in relation to MNFIs, which are the biggest users of tax havens and offshore finance. This paper investigates whether a unitary taxation approach which reflects economic reality would more easily and effectively ensure that the profits of MNFIs are taxed in the jurisdictions which give rise to those profits. It has previously been argued that the uniqueness of MNFIs results in a failure of the current system to accurately allocate profits and that unitary tax as an alternative could provide a sounder allocation model for international tax purposes. This paper goes a step further, and examines the practicalities of the implementation of unitary taxation for MNFIs in terms of the key components of such a regime, along with their their implications. This paper adopts a two-step approach in considering the implications of unitary taxation as a means of improved corporate tax coordination which requires international acceptance and agreement. First, the definitional issues of the unitary MNFI are examined and second, an appropriate allocation formula for this sector is investigated. To achieve this, the paper asks first, how the financial sector should be defined for the purposes of unitary taxation and what should constitute a unitary business for that sector and second, what is the ‘best practice’ model of an allocation formula for the purposes of the apportionment of the profits of the unitary business of a financial institution.

Distribution tap changer adjustment to improve small-scale embedded generator penetration and mitigate voltage rise

This paper addresses the voltage rise constraints that are initiated from increased renewable generation resources in low voltage distribution networks. In this paper, an approach which is able to mitigate these voltage rise constraints and allow for increased distributed generator penetration is presented. The proposed approach involves utilizing the distribution transformers static tap changer to reduce the distribution feeder voltage setpoint. The proposed approach is modeled on a generic low voltage distribution network using the PSS SINCAL© simulation software package and is also implemented in a real low voltage distribution network to verify its practicality. Results indicate that this approach can be implemented to mitigate the voltage rise constraint and increase small-scale embedded generator penetration in a high proportion of low voltage feeders while avoiding any substantial network costs.

Optimising the length of Random Breath Tests : results from the Queensland Community Engagement Trial

Research suggests that the length and quality of police-citizen encounters affect policing outcomes. The Koper Curve, for example, shows that the optimal length for police presence in hot spots is between 14 and 15 minutes, with diminishing returns observed thereafter. Our study, using data from the Queensland Community Engagement Trial (QCET), examines the impact of encounter length on citizen perceptions of police performance. QCET involved a randomised field trial, where 60 random breath test (RBT) traffic stop operations were randomly allocated to an experimental condition involving a procedurally just encounter or a business-as-usual control condition. Our results show that the optimal length of time for procedurally just encounters during RBT traffic stops is just less than 2 minutes. We show, therefore, that it is important to encourage and facilitate positive police–citizen encounters during RBTat traffic stops, while ensuring that the length of these interactions does not pass a point of diminishing returns.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Estimating hidden message length in binary image embedded by using boundary pixels steganography

In this paper, we propose a new steganalytic method to detect the message hidden in a black and white image using the steganographic technique developed by Liang, Wang and Zhang. Our detection method estimates the length of hidden message embedded in a binary image. Although the hidden message embedded is visually imperceptible, it changes some image statistic (such as inter-pixels correlation). Based on this observation, we first derive the 512 patterns histogram from the boundary pixels as the distinguishing statistic, then we compute the histogram difference to determine the changes of the 512 patterns histogram induced by the embedding operation. Finally we propose histogram quotient to estimate the length of the embedded message. Experimental results confirm that the proposed method can effectively and reliably detect the length of the embedded message.

Short-term changes in axial length during simulations of typical far, intermediate and near tasks

Purpose: To investigate the changes in axial length with the combined effect of accommodation and angle of gaze (convergence and downward gaze) over 5 minutes in groups of myopes and emmetropes. Methods: A total of 31 subjects (nine emmetropes, 10 low myopes, and 12 moderate to high myopes) aged from 18 to 31 years were recruited. To measure ocular biometrics in inferonasal gaze with accommodation, an optical biometer (Lenstar LS900) was inclined on a tilt and height adjustable stage, with the subject’s chinrest mounted on a rotary stage to induce various levels of convergence by rotation of the subject’s head in primary or downward gaze. Initially, the subjects performed a distance viewing task in primary gaze for 10 minutes to provide a ‘wash-out’ period for prior visual tasks, and then the subject’s axial length and ocular biometrics were measured in nine different combinations of gaze/accommodation over 5 minutes. These nine sessions for all gaze measurements (i.e. three levels of accommodation 9 three levels of convergence) were completed across 3 days of testing (one accommodation condition on each day).The nine combinations of gaze/accommodation were based on those required to view the centre, right and left edges of a distant TV at 6 m in primary gaze, an intermediate task (i.e. computer at 50 cm in 10° downward gaze) and a near task (i.e. reading A4 page at 20 cm in 20° downward gaze). Subjects were wearing a custom built three-axes head tracker throughout the experiment that monitored subjects’ relative head movements (roll, pitch and yaw) during measurements. Results: A significant increase in axial length occurred with the combined effect of accommodation, convergence and downward gaze (repeated measures ANOVA, p < 0.001), with the greatest axial elongation during the near task in downward gaze with convergence (i.e. downward 20°/inward 33°, with 5 D accommodation) (mean change 33 ± 13 lm, after 5 minutes task) followed by the intermediate task (i.e. downward 10°/inward 25°, with 2 D accommodation) (mean change 14 ± 11 lm, after 5 minutes task).Changes in axial length for the distance task (i.e. primary gaze/9° convergence, with 0.16 D accommodation) were not statistically significant (mean change 4 ± 8 lm, after 5 minutes task, p > 0.05). Moderate to high myopes had a greater change in the axial length (mean change 40 ± 11 lm after 5 minutes of near task) than that of emmetropes (mean change 29 ± 15 lm after 5 minutes of near task) and low myopes (mean change 29 ± 16 lm after 5 minutes of near task) associated with time (p = 0.02) and accommodation by time (p = 0.03). Conclusions: The combination of accommodation, convergence and downward angle has a significant short term effect on axial length over time. The near task in downward gaze with convergence caused a greater change in axial length than the intermediate and distant visual tasks. The greater axial elongation measured in the infero-nasal direction with accommodation is most likely associated with a combination of biomechanical factors such as, extraocular muscle forces and ciliary muscle contraction.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Survival models of community tenure and length of hospital stay for the seriously mentally ill : a 10-year perspective

Objective: To examine the effects of personal and community characteristics, specifically race and rurality, on lengths of state psychiatric hospital and community stays using maximum likelihood survival analysis with a special emphasis on change over a ten year period of time. Data Sources: We used the administrative data of the Virginia Department of Mental Health, Mental Retardation, and Substance Abuse Services (DMHMRSAS) from 1982-1991 and the Area Resources File (ARF). Given these two sources, we constructed a history file for each individual who entered the state psychiatric system over the ten year period. Histories included demographic, treatment, and community characteristics. Study Design: We used a longitudinal, population-based design with maximum likelihood estimation of survival models. We presented a random effects model with unobserved heterogeneity that was independent of observed covariates. The key dependent variables were lengths of inpatient stay and subsequent length of community stay. Explanatory variables measured personal, diagnostic, and community characteristics, as well as controls for calendar time. Data Collection: This study used secondary, administrative, and health planning data. Principal Findings: African-American clients leave the community more quickly than whites. After controlling for other characteristics, however, race does not affect hospital length of stay. Rurality does not affect length of community stays once other personal and community characteristics are controlled for. However, people from rural areas have longer hospital stays even after controlling for personal and community characteristics. The effects of time are significantly smaller than expected. Diagnostic composition effects and a decrease in the rate of first inpatient admissions explain part of this reduced impact of time. We also find strong evidence for the existence of unobserved heterogeneity in both types of stays and adjust for this in our final models. Conclusions: Our results show that information on client characteristics available from inpatient stay records is useful in predicting not only the length of inpatient stay but also the length of the subsequent community stay. This information can be used to target increased discharge planning for those at risk of more rapid readmission to inpatient care. Correlation across observed and unobserved factors affecting length of stay has significant effects on the measurement of relationships between individual factors and lengths of stay. Thus, it is important to control for both observed and unobserved factors in estimation.

Increasing the length of single-wall carbon nanotubes in a magnetically enhanced arc discharge

It is demonstrated that a magnetic field has a profound effect on the length of a single-wall carbon nanotube (SWCNT) synthesized in the arc discharge. The average length of SWCNT increases by a factor of 2 in discharge with magnetic field as compared with the discharge without magnetic field, and the yield of long nanotubes with lengths above 5 μm also increases. A model of SWCNT growth on metal catalyst in arc plasma was developed. Monte-Carlo simulations confirm that the increase of the plasma density in the magnetic field leads to an increase in the nanotube growth rate and thus leads to longer nanotubes.

Length control of He atmospheric plasma jet plumes: Effects of discharge parameters and ambient air

The effects of various discharge parameters and ambient gas on the length of He atmospheric plasma jet plumes expanding into the open air are studied. It is found that the voltage and width of the discharge-sustaining pulses exert significantly stronger effects on the plume length than the pulse frequency, gas flow rate, and nozzle diameter. This result is explained through detailed analysis of the I-V characteristics of the primary and secondary discharges which reveals the major role of the integrated total charges of the primary discharge in the plasma dynamics. The length of the jet plume can be significantly increased by guiding the propagating plume into a glass tube attached to the nozzle. This increase is attributed to elimination of the diffusion of surrounding air into the plasma plume, an absence which facilitates the propagation of the ionization front. These results are important for establishing a good level of understanding of the expansion dynamics and for enabling a high degree of control of atmospheric pressure plasmas in biomedical, materials synthesis and processing, environmental and other existing and emerging industrial applications. © 2009 American Institute of Physics.

Ways to increase the length of single wall carbon nanotubes in a magnetically enhanced arc discharge

Ability to control the properties of single-wall nanotubes produced in the arc discharge is important for many practical applications. Our experiments suggest that the length and purity of single-wall nanotubes significantly increase when the magnetic field is applied to the arc discharge. A model of a single wall carbon nanotube interaction and growth in the thermal plasma was developed which considers several important effects such as anode ablation that supplies the carbon plasma in an anodic arc discharge technique, and the momentum, charge and energy transfer processes between nanotube and plasma. The numerical simulations based on Monte-Carlo technique were performed, which explain an increase of the nanotubes produced in the magnetic field - enhanced arc discharge.