First-passage times for non-Markovian processes: Correlated impacts on a free process

We develop a method to obtain first-passage-time statistics for non-Markovian processes driven by dichotomous fluctuations. The fluctuations themselves need not be Markovian. We calculate analytic first-passage-time distributions and mean first-passage times for exponential, rectangular, and long-tail temporal distributions of the fluctuations.

Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

Absence of epidemic threshold in scale free networks with degree correlations

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbors degree, enforced by the degree detailed balance condition.

Giant acceleration of free diffusion by use of titled periodic potentials

The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as compared to free thermal diffusion with, for a realistic experimental setup, an enhancement of up to 14 orders of magnitude.

Free conjunctival autologous graft for bleb repair and bleb reduction after trabeculectomy and nonpenetrating filtering surgery.

PURPOSE: To describe methods and outcomes of excisional revision of a filtering bleb (bleb revision) using free conjunctival autologous graft either for bleb repair or for bleb reduction after trabeculectomy and deep sclerectomy with an implant. METHODS: Retrospective medical records were reviewed for a consecutive non-comparative case series comprising patients who underwent excisional revision of a filtering bleb between May 1998-January 2001. Excisional revision using free conjunctival autologous graft (bleb revision) was performed either for bleb repair, to treat early and late leaks and hypotony with maculopathy, or for bleb reduction, to improve ocular pain, discomfort, burning, foreign body sensation, tearing, and fluctuations of visual acuity. The revision consisted of bleb excision and free conjunctival autologous graft. The bleb histopathology was analyzed in patients who underwent bleb repair. RESULTS: Sixteen patients were included in the study, consisting of nine patients who had a trabeculectomy and seven patients who had a deep sclerectomy with an implant. Bleb revision was necessary in 14 patients due to leaking filtering bleb (bleb repair), and in 2 patients due to bleb dysesthesia (bleb reduction). After a follow-up of 15.1 +/- 8.4 months, the mean intraocular pressure (IOP) rose from 7.8 +/- 6.3 mm Hg to 14.3 +/- 6.5 mm Hg, and the visual acuity from 0.4 +/- 0.3 to 0.7 +/- 0.3, with a P value of 0.008 and 0.03, respectively. The complete success rate at 32 months, according to the Kaplan-Meier survival curve, was 38.3%, and the qualified success rate was 83.3%. Four patients (25%) required additional suturing for persistent bleb leak. To control IOP, antiglaucoma medical therapy was needed for six patients (37.5%) and repeated glaucoma surgery was needed for one patient. CONCLUSION: Free conjunctival autologous graft is a safe and successful procedure for bleb repair and bleb reduction. However, patients should be aware of the postoperative possibility of requiring medical or surgical intervention for IOP control after revision.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Synchronization in a lattice model of pulse-coupled oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interactions that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same as that obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.

Pulse wave analysis aortic pressure . distole should also be considered

La rigidité anormalement haute des artères à grande conductance est un marqueur de l'augmentation du risque cardiovasculaire et est typiquement retrouvée chez les patients diabétiques ou hypertendus. Ces vaisseaux deviennent plus rigides avec l'âge, expliquant la haute prévalence d'hypertension systolique chez les personnes âgées. Cette rigidification agit sur la pression sanguine de plusieurs façons. Notamment la fonction windkessel est gênée, menant à l'augmentation de la pression systolique et de la pression puisée, la diminution de la pression diastolique, et ainsi à l'augmentation de la postcharge ventriculaire gauche associée à une probable diminution de la perfusion coronarienne. De plus, la propagation des ondes de pression le long de l'arbre vasculaire est accélérée, de sorte que les ondes réfléchies générées au site de décalage d'impédance atteignent l'aorte ascendante plus tôt par rapport au début de l'éjection ventriculaire, aboutissant à une augmentation de la pression systolique centrale, ce qui n'arriverait pas en présence de vaisseaux moins rigides. Dans ce cas, au contraire, les ondes de pression antérogrades et réfléchies voyages plus lentement, de sorte que les ondes de réflexion tendent à atteindre l'aorte centrale une fois l'éjection terminée, augmentant la pression diastolique et contribuant à la perfusion coronarienne. La tonométrie d'applanation est une méthode non invasive permettant l'évaluation de la forme de l'onde de pression au niveau l'aorte ascendante, basée sur l'enregistrement du pouls périphérique, au niveau radial dans notre étude. Nous pouvons dériver à partir de cette méthode un index d'augmentation systolique (sAIX) qui révèle quel pourcentage de la pression centrale est du aux ondes réfléchies. Plusieurs études ont montré que cet index est corrélé à d'autres mesures de la rigidité artérielle comme la vitesse de l'onde de pouls, qu'il augmente avec l'âge et avec les facteurs de risques cardiovasculaires, et qu'il est capable de préciser le pronostic cardiovasculaire. En revanche, peu d'attention a été portée à l'augmentation de la pression centrale diastolique due aux ondes réfléchies (dAIX). Nous proposons donc de mesurer cet index par un procédé d'analyse développé dans notre laboratoire, et ce dans la même unité que l'index systolique. Etant donné que les modifications de la paroi artérielle modulent d'une part la vitesse de l'onde de pouls (PWV) et d'autre part le temps de voyage aller-retour des ondes de pression réfléchies aux sites de réflexion, toute augmentation de la quantité d'énergie réfléchie atteignant l'aorte pendant la systole devrait être associée à une diminution de l'énergie arrivant au même point pendant la diastole. Notre étude propose de mesurer ces deux index, ainsi que d'étudier la relation de l'index d'augmentation diastolique (dAIX) avec la vitesse de propagation de l'onde de pouls (PWV) et avec le rythme cardiaque (HR), ce dernier étant connu pour influencer l'index d'augmentation systolique (sAIX) . L'influence de la position couchée et assise est aussi étudiée. Les mesures de la PWV et des sAIX et dAIX est réalisée chez 48 hommes et 45 femmes âgées de 18 à 70 ans, classés en 3 groupes d'âges. Les résultats montrent qu'en fonction de l'âge, le genre et la position du corps, il y a une relation inverse entre sAIX et dAIX. Lorsque PWV et HR sont ajoutés comme covariables à un modèle de prédiction comprenant l'âge, le genre et la position du corps comme facteurs principaux, sAIX est directement lié à PWV (p<0.0001) et inversement lié à HR (p<0.0001). Avec la même analyse, dAIX est inversement lié à PWV (p<0.0001) et indépendant du rythme cardiaque (p=0.52). En conclusion, l'index d'augmentation diastolique est lié à la rigidité vasculaire au même degré que l'index d'augmentation systolique, alors qu'il est affranchi de l'effet confondant du rythme cardiaque. La quantification de l'augmentation de la pression aortique diastolique due aux ondes réfléchies pourrait être une partie utile de l'analyse de l'onde de pouls.

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a pefect agreement with numerical simulations.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators

We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.