990 resultados para Fractional Diffusion Equation


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In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

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Abstract This thesis proposes a set of adaptive broadcast solutions and an adaptive data replication solution to support the deployment of P2P applications. P2P applications are an emerging type of distributed applications that are running on top of P2P networks. Typical P2P applications are video streaming, file sharing, etc. While interesting because they are fully distributed, P2P applications suffer from several deployment problems, due to the nature of the environment on which they perform. Indeed, defining an application on top of a P2P network often means defining an application where peers contribute resources in exchange for their ability to use the P2P application. For example, in P2P file sharing application, while the user is downloading some file, the P2P application is in parallel serving that file to other users. Such peers could have limited hardware resources, e.g., CPU, bandwidth and memory or the end-user could decide to limit the resources it dedicates to the P2P application a priori. In addition, a P2P network is typically emerged into an unreliable environment, where communication links and processes are subject to message losses and crashes, respectively. To support P2P applications, this thesis proposes a set of services that address some underlying constraints related to the nature of P2P networks. The proposed services include a set of adaptive broadcast solutions and an adaptive data replication solution that can be used as the basis of several P2P applications. Our data replication solution permits to increase availability and to reduce the communication overhead. The broadcast solutions aim, at providing a communication substrate encapsulating one of the key communication paradigms used by P2P applications: broadcast. Our broadcast solutions typically aim at offering reliability and scalability to some upper layer, be it an end-to-end P2P application or another system-level layer, such as a data replication layer. Our contributions are organized in a protocol stack made of three layers. In each layer, we propose a set of adaptive protocols that address specific constraints imposed by the environment. Each protocol is evaluated through a set of simulations. The adaptiveness aspect of our solutions relies on the fact that they take into account the constraints of the underlying system in a proactive manner. To model these constraints, we define an environment approximation algorithm allowing us to obtain an approximated view about the system or part of it. This approximated view includes the topology and the components reliability expressed in probabilistic terms. To adapt to the underlying system constraints, the proposed broadcast solutions route messages through tree overlays permitting to maximize the broadcast reliability. Here, the broadcast reliability is expressed as a function of the selected paths reliability and of the use of available resources. These resources are modeled in terms of quotas of messages translating the receiving and sending capacities at each node. To allow a deployment in a large-scale system, we take into account the available memory at processes by limiting the view they have to maintain about the system. Using this partial view, we propose three scalable broadcast algorithms, which are based on a propagation overlay that tends to the global tree overlay and adapts to some constraints of the underlying system. At a higher level, this thesis also proposes a data replication solution that is adaptive both in terms of replica placement and in terms of request routing. At the routing level, this solution takes the unreliability of the environment into account, in order to maximize reliable delivery of requests. At the replica placement level, the dynamically changing origin and frequency of read/write requests are analyzed, in order to define a set of replica that minimizes communication cost.

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In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

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The integration of the differential equation of the second law of Fick applied to the diffusion of chemical elements in a semi-infinite solid made it easier to estimate the time of stay of olivine mega-cristals in contact with the host lava The results of this research show the existence of two groups of olivine. The first remained in contact with the magmatic liquid during 19 to 22 days, while the second remained so during only 5 to 9 days. This distinction is correlative to that based on the qualitative observation.

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A recent finding of the structural VAR literature is that the response of hours worked to a technology shock depends on the assumption on the order of integration of the hours. In this work we relax this assumption, allowing for fractional integration and long memory in the process for hours and productivity. We find that the sign and magnitude of the estimated impulse responses of hours to a positive technology shock depend crucially on the assumptions applied to identify them. Responses estimated with short-run identification are positive and statistically significant in all datasets analyzed. Long-run identification results in negative often not statistically significant responses. We check validity of these assumptions with the Sims (1989) procedure, concluding that both types of assumptions are appropriate to recover the impulse responses of hours in a fractionally integrated VAR. However, the application of longrun identification results in a substantial increase of the sampling uncertainty. JEL Classification numbers: C22, E32. Keywords: technology shock, fractional integration, hours worked, structural VAR, identification

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Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumor (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT. Methods and materials: Five patients (3W/2M, aged 56 ± 13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analyzed blindly, then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analyzed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analyzed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2 ± 7.7 g/mL to 5.9 ± 5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

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Introduction: According to guidelines, patients with coronary artery disease (CAD) should undergo revascularization if myocardial ischemia is present. While coronary angiography (CXA) allows the morphological assessment of CAD, the fractional flow reserve (FFR) has proved to be a complementary invasive test to assess the functional significance of CAD, i.e. to detect ischemia. Perfusion Cardiac Magnetic Resonance (CMR) has turned out to be a robust non-invasive technique to assess myocardial ischemia. The objective: is to compare the cost-effectiveness ratio - defined as the costs per patient correctly diagnosed - of two algorithms used to diagnose hemodynamically significant CAD in relation to the pretest likelihood of CAD: 1) aCMRto assess ischemia before referring positive patients to CXA (CMR + CXA), 2) a CXA in all patients combined with a FFR test in patients with angiographically positive stenoses (CXA + FFR). Methods: The costs, evaluated from the health care system perspective in the Swiss, German, the United Kingdom (UK) and the United States (US) contexts, included public prices of the different tests considered as outpatient procedures, complications' costs and costs induced by diagnosis errors (false negative). The effectiveness criterion wasthe ability to accurately identify apatient with significantCAD.Test performancesused in the model were based on the clinical literature. Using a mathematical model, we compared the cost-effectiveness ratio for both algorithms for hypothetical patient cohorts with different pretest likelihood of CAD. Results: The cost-effectiveness ratio decreased hyperbolically with increasing pretest likelihood of CAD for both strategies. CMR + CXA and CXA + FFR were equally costeffective at a pretest likelihood of CAD of 62% in Switzerland, 67% in Germany, 83% in the UK and 84% in the US with costs of CHF 5'794, Euros 1'472, £ 2'685 and $ 2'126 per patient correctly diagnosed. Below these thresholds, CMR + CXA showed lower costs per patient correctly diagnosed than CXA + FFR. Implications for the health care system/professionals/patients/society These results facilitate decision making for the clinical use of new generations of imaging procedures to detect ischemia. They show to what extent the cost-effectiveness to diagnose CAD depends on the prevalence of the disease.

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High Resolution Magic Angle Spinning (HR-MAS) NMR allows metabolic characterization of biopsies. HR-MAS spectra from tissues of most organs show strong lipid contributions that are overlapping metabolite regions, which hamper metabolite estimation. Metabolite quantification and analysis would benefit from a separation of lipids and small metabolites. Generally, a relaxation filter is used to reduce lipid contributions. However, the strong relaxation filter required to eliminate most of the lipids also reduces the signals for small metabolites. The aim of our study was therefore to investigate different diffusion editing techniques in order to employ diffusion differences for separating lipid and small metabolite contributions in the spectra from different organs for unbiased metabonomic analysis. Thus, 1D and 2D diffusion measurements were performed, and pure lipid spectra that were obtained at strong diffusion weighting (DW) were subtracted from those obtained at low DW, which include both small metabolites and lipids. This subtraction yielded almost lipid free small metabolite spectra from muscle tissue. Further improved separation was obtained by combining a 1D diffusion sequence with a T2-filter, with the subtraction method eliminating residual lipids from the spectra. Similar results obtained for biopsies of different organs suggest that this method is applicable in various tissue types. The elimination of lipids from HR-MAS spectra and the resulting less biased assessment of small metabolites have potential to remove ambiguities in the interpretation of metabonomic results. This is demonstrated in a reproducibility study on biopsies from human muscle.

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Object The purpose of this study was to investigate whether diffusion tensor imaging (DTI) of the corticospinal tract (CST) is a reliable surrogate for intraoperative macrostimulation through the deep brain stimulation (DBS) leads. The authors hypothesized that the distance on MRI from the DBS lead to the CST as determined by DTI would correlate with intraoperative motor thresholds from macrostimulations through the same DBS lead. Methods The authors retrospectively reviewed pre- and postoperative MRI studies and intraoperative macrostimulation recordings in 17 patients with Parkinson disease (PD) treated by DBS stimulation. Preoperative DTI tractography of the CST was coregistered with postoperative MRI studies showing the position of the DBS leads. The shortest distance and the angle from each contact of each DBS lead to the CST was automatically calculated using software-based analysis. The distance measurements calculated for each contact were evaluated with respect to the intraoperative voltage thresholds that elicited a motor response at each contact. Results There was a nonsignificant trend for voltage thresholds to increase when the distances between the DBS leads and the CST increased. There was a significant correlation between the angle and the voltage, but the correlation was weak (coefficient of correlation [R] = 0.36). Conclusions Caution needs to be exercised when using DTI tractography information to guide DBS lead placement in patients with PD. Further studies are needed to compare DTI tractography measurements with other approaches such as microelectrode recordings and conventional intraoperative MRI-guided placement of DBS leads.

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PURPOSE: To assess the inter/intraobserver variability of apparent diffusion coefficient (ADC) measurements in treated hepatic lesions and to compare ADC measurements in the whole lesion and in the area with the most restricted diffusion (MRDA). MATERIALS AND METHODS: Twenty-five patients with treated malignant liver lesions were examined on a 3.0T machine. After agreeing on the best ADC image, two readers independently measured the ADC values in the whole lesion and in the MRDA. These measurements were repeated 1 month later. The Bland-Altman method, Spearman correlation coefficients, and the Wilcoxon signed-rank test were used to evaluate the measurements. RESULTS: Interobserver variability for ADC measurements in the whole lesion and in the MRDA was 0.17 x 10(-3) mm(2)/s [-0.17, +0.17] and 0.43 x 10(-3) mm(2)/s [-0.45, +0.41], respectively. Intraobserver limits of agreement could be as low as [-0.10, +0.12] 10(-3) mm(2)/s and [-0.20, +0.33] 10(-3) mm(2)/s for measurements in the whole lesion and in the MRDA, respectively. CONCLUSION: A limited variability in ADC measurements does exist, and it should be considered when interpreting ADC values of hepatic malignancies. This is especially true for the measurements of the minimal ADC.

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Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumour (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT Methods and Materials: Five patients (3 W/2M, aged 56±13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analysed blindly and then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analysed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analysed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2±7.7 g/mL to 5.9±5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

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Purpose: To evaluate the short- and mid-term evolutions of the apparent diffusion coefficient of lesions treated with RF, in order to determine if the ADC can be used as a marker of tumour response. Methods and Materials: Twenty patients were treated for a liver malignancy with RF and were examined on a 1.5 T/3.0 T machine with T2, gadolinium-enhanced T1 and diffusion sequences: before treatment (< 1 month), just after treatment (< 1 month) and midterm (3-6 months). The ADC was measured in the whole lesion and in the area with the most restricted diffusion (MRDA). The ROI size was also measured on the diffusion map. The Pearson/ANOVA tests were used. Results: All patients were successfully treated with complete disappearance of CE. The lesional size on T2 showed a negative evolution in time (p < 0.002). The ADC in the whole lesion showed a bell-shaped evolution (increasing just after RF, then decreasing, p = 0.02). The ROI size on the diffusion map followed a similar course (p = 0.01). For the MRDA, such evolutions were also found, but they were not significant. There was a negative correlation between CE and the ADC (p < 0.02) and between the lesional size on T2 and ADC (p = 0.03) in the whole lesion. There were also positive correlations between the ROI size and ADC (p = 0.0008) and between CE and the size on T2 (p = 0.0002). The ADC in MRDA showed some non-significant correlations with other variables. Conclusion: The lesions successfully treated with RF have a clear and predictable evolution in terms of T2 size, CE and ADC.