Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields.

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools. Copyright © 2013 John Wiley & Sons, Ltd.

Measuring the diffusion of palliative care in long-term care facilities - a death census

ABSTRACT: BACKGROUND: The dissemination of palliative care for patients presenting complex chronic diseases at various stages has become an important matter of public health. A death census in Swiss long-term care facilities (LTC) was set up with the aim of monitoring the frequency of selected indicators of palliative care. METHODS: The survey covered 150 LTC facilities (105 nursing homes and 45 home health services), each of which was asked to complete a questionnaire for every non-accidental death over a period of six months. The frequency of 4 selected indicators of palliative care (resort to a specialized palliative care service, the administration of opiates, use of any pain measurement scale or other symptom measurement scale) was monitored in respect of the stages of care and analysed based on gender, age, medical condition and place of residence. RESULTS: Overall, 1200 deaths were reported, 29.1% of which were related to cancer. The frequencies of each indicator varied according to the type of LTC, mostly regarding the administration of opiate. It appeared that the access to palliative care remained associated with cancer, terminal care and partly with age, whereas gender and the presence of mental disorders had no effect on the indicators. In addition, the use of drugs was much more frequent than the other indicators. CONCLUSION: The profile of patients with access to palliative care must become more diversified. Among other recommendations, equal access to opiates in nursing homes and in home health services, palliative care at an earlier stage and the systematic use of symptom management scales when resorting to opiates have to become of prime concern.

Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

The Global Diffusion of Regulatory Agencies: Channels of Transfer and Stages of Diffusion

The autonomous regulatory agency has recently become the ‘appropriate model’ of governance across countries and sectors. The dynamics of this process is captured in our data set, which covers the creation of agencies in 48 countries and 16 sectors since the 1920s. Adopting a diffusion approach to explain this broad process of institutional change, we explore the role of countries and sectors as sources of institutional transfer at different stages of the diffusion process. We demonstrate how the restructuring of national bureaucracies unfolds via four different channels of institutional transfer. Our results challenge theoretical approaches that overemphasize the national dimension in global diffusion and are insensitive to the stages of the diffusion process. Further advance in study of diffusion depends, we assert, on the ability to apply both cross-sectoral and cross-national analysis to the same research design and to incorporate channels of transfer with different causal mechanisms for different stages of the diffusion process.

Mean platelet volume in the early phase of acute ischemic stroke is not associated with severity or functional outcome.

Background: Previous studies reported an increase of mean platelet volume (MPV) in patients with acute ischemic stroke. However, its correlation with stroke severity has not been investigated. Moreover, studies on the association of MPV with functional outcome yielded inconsistent results. Methods: We included all consecutive ischemic stroke patients admitted to CHUV (Centre Hospitalier Universitaire Vaudois) Neurology Service within 24 h after stroke onset who had MPV measured on admission. The association of MPV with stroke severity (NIHSS score at admission and at 24 h) and outcome (Rankin Scale score at 3 and 12 months) was analyzed in univariate analysis. The chi(2) test was performed to compare the frequency of minor strokes (NIHSS score </=4) and good functional outcome (Rankin Scale score </=2) across MPV quartiles. The ANOVA test was used to compare MPV between stroke subtypes according to the TOAST classification. Student's two-tailed unpaired t test was performed to compare MPV between lacunar and nonlacunar strokes. MPV was generated at admission by the Sysmex XE-2100 automated cell counter (Sysmex Corporation, Kobe, Japan) from EDTA blood samples. Results: There was no significant difference in the frequency of minor strokes (p = 0.46) and good functional outcome (p = 0.06) across MPV quartiles. MPV was not associated with stroke severity or outcome in univariate analysis. There was no significant difference in MPV between stroke subtypes according to the TOAST classification (p = 0.173) or between lacunar and nonlacunar strokes (10.50 +/- 0.91 vs. 10.40 +/- 0.81 fl, p = 0.322). Conclusions: MPV, assessed within 24 h after ischemic stroke onset, is not associated with stroke severity or functional outcome.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Systemic effects of epidural Methylprednisolone injection on glucose tolerance in diabetic patients.

ABSTRACT: BACKGROUND: Several studies have shown that in diabetic patients, the glycemic profile was disturbed after intra-articular injection of corticosteroids. Little is known about the impact of epidural injection in such patients. The goal of this study was double, at first comparing the glycaemic profile in diabetic patients after a unique injection of 80 mg of acetate methylprednisolone either intra-articular or epidural and secondly to compare the amount of systemic diffusion of the drug after both procedures. METHODS: Seventeen patients were included. Glycemic changes were compared in 9 diabetic patients following intra-articular (4 patients) and epidural injections (5 patients). Epidural injections were performed using the sacral route under fluoroscopic control in patients with lumbar spinal stenosis. Diabetes control had to stable for more than 10 days and the renal function to be preserved. Blood glucose was monitored using a validated continuous measuring device (GMS, Medtronic) the day before and for two days following the injection. Results were expressed in the form of daily glycemic profiles and as by mean, peak and minimal values +/ SD. The urinary excretion of methylprednisolone after the 2 routes of injection was analyzed in 8 patients (4 in each group). Urine samples were cropped one hour before the injections, then 4 times during the first day and 3 times a week for 2 weeks. The measurements included the free and conjugated fraction RESULTS: The glycaemic profile remains unchanged with no significant changes in the group of the 5 diabetic patients receiving epidural injections. On the other end, the average peak and mean values were enhanced up to 3 mmol/l above baseline two days after the infiltration in the groups of the 4 diabetic patients infiltrated intra-articular. The mean urinary excretion of the steroid was about ten times higher in the intra-articular versus epidural group: 7000 ng/ml versus 700 ng/ml. Looking at each individual there were marked differences especially after intra-articular injections. CONCLUSION: This is the first study to show that a single epidural steroid injection of 80 mg depot methylprednisolone had no effect on the glycemic control in diabetic patients. The absence of glycemic control changes correlated well with the very low urinary excretion of the drug after epidural injection. Trial registration NCT01420497.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Mean-payoff games and propositional proofs

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