Continuous-time formulation of reaction-diffusion processes on heterogeneous metapopulations

We present the derivation of the continuous-time equations governing the limit dynamics of discrete-time reaction-diffusion processes defined on heterogeneous metapopulations. We show that, when a rigorous time limit is performed, the lack of an epidemic threshold in the spread of infections is not limited to metapopulations with a scale-free architecture, as it has been predicted from dynamical equations in which reaction and diffusion occur sequentially in time

131I/123I-metaiodobenzylguanidine (mIBG) scintigraphy: procedure guidelines for tumour imaging.

The aim of this document is to provide general information about mIBG scintigraphy in cancer patients. The guidelines describe the mIBG scintigraphy protocol currently used in clinical routine, but do not include all existing procedures for neuroendocrine tumours. The guidelines should therefore not be taken as exclusive of other nuclear medicine modalities that can be used to obtain comparable results. It is important to remember that the resources and facilities available for patient care may vary from one country to another and from one medical institution to another. The present guidelines have been prepared for nuclear medicine physicians and intend to offer assistance in optimizing the diagnostic information that can currently be obtained from mIBG scintigraphy. The corresponding guidelines of the Society of Nuclear Medicine (SNM) and the Dosimetry, Therapy and Paediatric Committee of the EANM have been taken into consideration, and partially integrated into this text. The same has been done with the most relevant literature on this topic, and the final result has been discussed within a group of distinguished experts.

Dynamical features of reaction-diffusion fronts in fractals

The speed of front propagation in fractals is studied by using (i) the reduction of the reaction-transport equation into a Hamilton-Jacobi equation and (ii) the local-equilibrium approach. Different equations proposed for describing transport in fractal media, together with logistic reaction kinetics, are considered. Finally, we analyze the main features of wave fronts resulting from this dynamic process, i.e., why they are accelerated and what is the exact form of this acceleration

Effect of initial conditions on the speed of reaction-diffusion fronts

The effect of initial conditions on the speed of propagating fronts in reaction-diffusion equations is examined in the framework of the Hamilton-Jacobi theory. We study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion. Nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

Fracture imaging within a granitic rock aquifer using multiple-offset single-hole and cross-hole GPR reflection data

The sparsely spaced highly permeable fractures of the granitic rock aquifer at Stang-er-Brune (Brittany, France) form a well-connected fracture network of high permeability but unknown geometry. Previous work based on optical and acoustic logging together with single-hole and cross-hole flowmeter data acquired in 3 neighbouring boreholes (70-100 m deep) has identified the most important permeable fractures crossing the boreholes and their hydraulic connections. To constrain possible flow paths by estimating the geometries of known and previously unknown fractures, we have acquired, processed and interpreted multifold, single- and cross-hole GPR data using 100 and 250 MHz antennas. The GPR data processing scheme consisting of timezero corrections, scaling, bandpass filtering and F-X deconvolution, eigenvector filtering, muting, pre-stack Kirchhoff depth migration and stacking was used to differentiate fluid-filled fracture reflections from source generated noise. The final stacked and pre-stack depth-migrated GPR sections provide high-resolution images of individual fractures (dipping 30-90°) in the surroundings (2-20 m for the 100 MHz antennas; 2-12 m for the 250 MHz antennas) of each borehole in a 2D plane projection that are of superior quality to those obtained from single-offset sections. Most fractures previously identified from hydraulic testing can be correlated to reflections in the single-hole data. Several previously unknown major near vertical fractures have also been identified away from the boreholes.

Phase-sensitive black-blood coronary vessel wall imaging.

Black-blood MR coronary vessel wall imaging may become a powerful tool for the quantitative and noninvasive assessment of atherosclerosis and positive arterial remodeling. Although dual-inversion recovery is currently the gold standard, optimal lumen-to-vessel wall contrast is sometimes difficult to obtain, and the time window available for imaging is limited due to competing requirements between blood signal nulling time and period of minimal myocardial motion. Further, atherosclerosis is a spatially heterogeneous disease, and imaging at multiple anatomic levels of the coronary circulation is mandatory. However, this requirement of enhanced volumetric coverage comes at the expense of scanning time. Phase-sensitive inversion recovery has shown to be very valuable for enhancing tissue-tissue contrast and for making inversion recovery imaging less sensitive to tissue signal nulling time. This work enables multislice black-blood coronary vessel wall imaging in a single breath hold by extending phase-sensitive inversion recovery to phase-sensitive dual-inversion recovery, by combining it with spiral imaging and yet relaxing constraints related to blood signal nulling time and period of minimal myocardial motion.

Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Reaction-diffusion wave fronts: Multigeneration biological species under climate change

A generalization of reaction-diffusion models to multigeneration biological species is presented. It is based on more complex random walks than those in previous approaches. The new model is developed analytically up to infinite order. Our predictions for the speed agree to experimental data for several butterfly species better than existing models. The predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Added prognostic value of myocardial blood flow quantitation in rubidium-82 positron emission tomography imaging

Les maladies cardiovasculaires restent la cause de mortalité la plus élevée dans le monde occidental. Il s'agit d'un processus long et complexe, dont l'infarctus du myocarde et la mort cardiaque ne sont que la fin d'un spectrum. La perfusion myocardique joue un rôle central dans l'évolution de la maladie et survient chronologiquement en amont de la dysfonction diastolique et systolique, ainsi que de l'infarctus du myocarde. Une meilleure compréhension de la Physiopathologie sous-jacente est cruciale dans le diagnostique et la prise en charge du patient. Dans ce sens, ce travail tente d'évaluer l'apport de l'évaluation de la perfusion myocardique évaluée par la tomographic à émission de positron (PET/CT) quant à la prédiction d'événements cardiovasculaires. De plus, l'apport de l'évaluation quantitative par rapport à l'évaluation qualitative a été démontré dans ce travail. Nous avons utilisé un radiotraceur unique au regard de ses caractéristiques. En effet, Le Rubidium-82 est un traceur qui ne nécessite pas d'un cyclotron pour sa fabrication, dès lors qu'il est produit par un générateur, rendant ainsi sa disponibilité un atout et un avantage potentiel lors de futurs implémentations à plus grande échelle. Ce travail démontre la supériorité de l'analyse de perfusion myocardique quantitative par rapport à l'analyse traditionnelle qualitative, ce qui n'était pas encore confirmé avec le Rubidium-82. Les résultats montrent une démarcation significative entre les différentes valeurs de perfusion quantitative/absolue, permettant de distinguer différentes populations plus ou moins à risque en terme de prédiction d'événements cardiaques futurs. Il est intéressant de noter que dans un modèle combinant l'analyse qualitative et quantitative proposé dans ce travail, l'inclusion des résultats les plus ischémiques obtenus par l'analyse qualitative avec les résultats de perfusion les plus bas en terme de flux myocardique absolu (analyse quantitative) démarque une population à très bas risque d'événements cardiovasculaires majeurs, une prédiction pouvant être observée surplus de 1'000 jours. Ces résultats forment un ajout significatif quant à l'évaluation de la perfusion myocardique par la médecine nucléaire, notamment par ce model intégratif proposé, lequel permet une prédiction précise et contributive dans le cadre de futurs événements cardiovasculaires majeurs.

Reaction-diffusion waves of advance in the transition to agricultural economics

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

Tree-based message diffusion for managing replicated data in unreliable and resource-constrained peer-to-peer environment

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.