Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

WT1 interacts with MAD2 and regulates mitotic checkpoint function

Tumour suppressors safeguard the fidelity of the mitotic checkpoint by transcriptional regulation of genes that encode components of the mitotic checkpoint complex (MCC). Here we report a new role for the tumour suppressor and transcription factor, WT1, in the mitotic checkpoint. We show that WT1 regulates the MCC by directly interacting with the spindle assembly checkpoint protein, MAD2. WT1 colocalizes with MAD2 during mitosis and preferentially binds to the functionally active, closed-conformer, C-MAD2. Furthermore, WT1 associates with the MCC containing MAD2, BUBR1 and CDC20, resulting in prolonged inhibition of the anaphase-promoting complex/cyclosome (APC/C) and delayed degradation of its substrates SECURIN and CYCLIN B1. Strikingly, RNA interference-mediated depletion of WT1 leads to enhanced turnover of SECURIN, decreased lag time to anaphase and defects in chromosome segregation. Our findings identify WT1 as a regulator of the mitotic checkpoint and chromosomal stability.

Charge mediated semiconducting-to-metallic phase transition in molybdenum disulfide monolayer and hydrogen evolution reaction in new 1T′ phase

The phase transition of single layer molybdenum disulfide (MoS2) from semiconducting 2H to metallic 1T and then to 1T′ phases, and the effect of the phase transition on hydrogen evolution reaction (HER) are investigated within this work by density functional theory. Experimentally, 2H-MoS2 has been widely used as an excellent electrode for HER and can get charged easily. Here we find that the negative charge has a significant impact on the structural phase transition in a MoS2 monolayer. The thermodynamic stability of 1T-MoS2 increases with the negative charge state, comparing with the 2H-MoS2 structure before phase transition and the kinetic energy barrier for a phase transition from 2H to 1T decreases from 1.59 to 0.27 eV when 4e– are injected per MoS2 unit. Additionally, 1T phase is found to transform into the distorted structure (1T′ phase) spontaneously. On their activity toward hydrogen evolution reaction, 1T′-MoS2 structure shows comparable hydrogen evolution reaction activity to the 2H-MoS2 structure. If the charge transfer kinetics is taken into account, the catalytic activity of 1T′-MoS2 is superior to that of 2H-MoS2. Our finding provides a possible novel method for phase transition of MoS2 and enriches understanding of the catalytic properties of MoS2 for HER.

IT consumerization and its effects on IT business value, IT capabilities, and the IT function

IT consumerization is both a major opportunity and significant challenge for organizations. However, IS research has hardly discussed the implications for IT management so far. In this paper we address this topic by empirically identifying organizational themes for IT consumerization and conceptually exploring the direct and indirect effects on the business value of IT, IT capabilities, and the IT function. More specifically, based on two case studies, we identify eight organizational themes: consumer IT strategy, policy development and responsibilities, consideration of private life of employees, user involvement into IT-related processes, individualization, updated IT infrastructure, end user support, and data and system security. The contributions of this paper are: (1) the identification of organizational themes for IT consumerization; (2) the proposed effects on the business value of IT, IT capabilities and the IT function, and; (3) combining empirical insights into IT consumerization with managerial theories in the IS discipline.

Understanding the function and mechanisms of intestinal cell kinase in the growth and survival of prostate cancer cells

This project was a step forward in discovering the potential role of intestinal cell kinase in prostate cancer development. Intestinal cell kinase was shown to be upregulated in prostate cancer cells and altered expression led to changes in key cell survival proteins. This study used in vitro experiments to monitor changes in cell growth, protein and RNA expression.

Cross-cultural adaptation and validation of the Foot Function Index to Spanish

Background The purpose of this study was to adapt and validate the Foot Function Index to the Spanish (FFI-Sp) following the guidelines of the American Academy of Orthopaedic Surgeons. Methods A cross-sectional study 80 participants with some foot pathology. A statistical analysis was made, including a correlation study with other questionnaires (the Foot Health Status Questionnaire, EuroQol 5-D, Visual Analogue Pain Scale, and the Short Form SF-12 Health Survey). Data analysis included reliability, construct and criterion-related validity and factor analyses. Results The principal components analysis with varimax rotation produced 3 principal factors that explained 80% of the variance. The confirmatory factor analysis showed an acceptable fit with a comparative fit index of 0.78. The FFI-Sp demonstrated excellent internal consistency on the three subscales: pain 0.95; disability 0.96; and activity limitation 0.69, the subscale that scored lowest. The correlation between the FFI-Sp and the other questionnaires was high to moderate. Conclusions The Spanish version of the Foot Function Index (FFI-Sp) is a tool that is a valid and reliable tool with a very good internal consistency for use in the assessment of pain, disability and limitation of the function of the foot, for use both in clinic and research.

A kinematic analysis of the hand function

Background The evaluation of the hand function is an essential element within the clinical practice. The usual assessments are focus on the ability to perform activities of daily life. The inclusion of instruments to measure kinematic variables provides a new approach to the assessment. Inertial sensors adapted to the hand could be used as a complementary instrument to the traditional assessment. Material: clinimetric assessment (Upper Limb Functional Index, Quick Dash), antrophometric variables (eight and weight), dynamometry (palm preasure) was taken. Functional analysis was made with Acceleglove system for the right hand and computer system. The glove has six acceleration sensor, one on each finger and another one on the reverse palm. Method Analytic, transversal approach. Ten healthy subject made six task on evaluation table (tripod pinch, lateral pinch and tip pinch, extension grip, spherical grip and power grip). Each task was made and measure three times, the second one was analyze for the results section. A Matlab script was created for the analysis of each movement and detection phase based on module vector. Results The module acceleration vector offers useful information of the hand function. The data analysis obtained during the performance of functional gestures allows to identify five different phases within the movement, three static phase and tow dynamic, each module vector was allied to one task. Conclusion Module vector variables could be used for the analysis of the different task made by the hand. Inertial sensor could be use as a complement for the traditional assessment system.

Probabilistic multi-tensor estimation using the tensor distribution function

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve crossing fiber tracts. Recently, a number of high-angular resolution schemes with greater than 6 gradient directions have been employed to address this issue. In this paper, we introduce the Tensor Distribution Function (TDF), a probability function defined on the space of symmetric positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the diffusion orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function.

Identifying rate-limiting nodes in large-scale cortical networks for visuospatial processing: An illustration using fMRI

With the advent of functional neuroimaging techniques, in particular functional magnetic resonance imaging (fMRI), we have gained greater insight into the neural correlates of visuospatial function. However, it may not always be easy to identify the cerebral regions most specifically associated with performance on a given task. One approach is to examine the quantitative relationships between regional activation and behavioral performance measures. In the present study, we investigated the functional neuroanatomy of two different visuospatial processing tasks, judgement of line orientation and mental rotation. Twenty-four normal participants were scanned with fMRI using blocked periodic designs for experimental task presentation. Accuracy and reaction time (RT) to each trial of both activation and baseline conditions in each experiment was recorded. Both experiments activated dorsal and ventral visual cortical areas as well as dorsolateral prefrontal cortex. More regionally specific associations with task performance were identified by estimating the association between (sinusoidal) power of functional response and mean RT to the activation condition; a permutation test based on spatial statistics was used for inference. There was significant behavioral-physiological association in right ventral extrastriate cortex for the line orientation task and in bilateral (predominantly right) superior parietal lobule for the mental rotation task. Comparable associations were not found between power of response and RT to the baseline conditions of the tasks. These data suggest that one region in a neurocognitive network may be most strongly associated with behavioral performance and this may be regarded as the computationally least efficient or rate-limiting node of the network.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

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.

Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller–Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥sqrt(2δ) in the F-KPP equation.

The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Developments of the total entropy utility function for the dual purpose of model discrimination and parameter estimation in Bayesian design

The total entropy utility function is considered for the dual purpose of Bayesian design for model discrimination and parameter estimation. A sequential design setting is proposed where it is shown how to efficiently estimate the total entropy utility for a wide variety of data types. Utility estimation relies on forming particle approximations to a number of intractable integrals which is afforded by the use of the sequential Monte Carlo algorithm for Bayesian inference. A number of motivating examples are considered for demonstrating the performance of total entropy in comparison to utilities for model discrimination and parameter estimation. The results suggest that the total entropy utility selects designs which are efficient under both experimental goals with little compromise in achieving either goal. As such, the total entropy utility is advocated as a general utility for Bayesian design in the presence of model uncertainty.

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.