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We analyze a general class of difference operators H(epsilon) = T(epsilon) + V(epsilon) on l(2)((epsilon Z)(d)), where V(epsilon) is a one-well potential and epsilon is a small parameter. We construct formal asymptotic expansions of WKB-type for eigenfunctions associated with the low lying eigenvalues of H(epsilon). These are obtained from eigenfunctions or quasimodes for the operator H(epsilon), acting on L(2)(R(d)), via restriction to the lattice (epsilon Z)(d).
Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average-local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.
We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.
During preclinical development of a gestagenic drug, a significant increase of the total plasma concentration was observed after multiple dosing in pregnant rabbits, but not in (non-pregnant) rats or monkeys. We used a PBPK modeling approach in combination with in vitro and in vivo data to address the question to what extent the pharmacologically active free drug concentration is affected by pregnancy induced processes. In human, a significant increase in sex hormone binding globulin (SHBG), and an induction of hepatic CYP3A4 as well as plasma esterases is observed during pregnancy. We find that the observed increase in total plasma trough levels in rabbits can be explained as a combined result of (i) drug accumulation due to multiple dosing, (ii) increase of the binding protein SHBG, and (iii) clearance induction. For human, we predict that free drug concentrations in plasma would not increase during pregnancy above the steady state trough level for non-pregnant women.
The human immunodeficiency virus (HIV) can be suppressed by highly active anti-retroviral therapy (HAART) in the majority of infected patients. Nevertheless, treatment interruptions inevitably result in viral rebounds from persistent, latently infected cells, necessitating lifelong treatment. Virological failure due to resistance development is a frequent event and the major threat to treatment success. Currently, it is recommended to change treatment after the confirmation of virological failure. However, at the moment virological failure is detected, drug resistant mutants already replicate in great numbers. They infect numerous cells, many of which will turn into latently infected cells. This pool of cells represents an archive of resistance, which has the potential of limiting future treatment options. The objective of this study was to design a treatment strategy for treatment-naive patients that decreases the likelihood of early treatment failure and preserves future treatment options. We propose to apply a single, pro-active treatment switch, following a period of treatment with an induction regimen. The main goal of the induction regimen is to decrease the abundance of randomly generated mutants that confer resistance to the maintenance regimen, thereby increasing subsequent treatment success. Treatment is switched before the overgrowth and archiving of mutant strains that carry resistance against the induction regimen and would limit its future re-use. In silico modelling shows that an optimal trade-off is achieved by switching treatment at & 80 days after the initiation of antiviral therapy. Evaluation of the proposed treatment strategy demonstrated significant improvements in terms of resistance archiving and virological response, as compared to conventional HAART. While continuous pro-active treatment alternation improved the clinical outcome in a randomized trial, our results indicate that a similar improvement might also be reached after a single pro-active treatment switch. The clinical validity of this finding, however, remains to be shown by a corresponding trial.
Asymptotic first exit times of the chafee-infante equation with small heavy-tailed levy noise
(2011)
This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump Levy noise in the limit of small noise intensity. It is shown that the law of the suitably renormalized first exit times from the domain of attraction of a stable state converges to an exponential law of parameter 1 in a strong sense of Laplace transforms, including exponential moments. As a consequence, the expected exit times increase polynomially in the inverse intensity, in contrast to Gaussian perturbations, where this growth is known to be of exponential rate.
The goal of this paper is to establish the existence of a foliation of the asymptotic region of an asymptotically flat manifold with positive mass by surfaces which are critical points of the Willmore functional subject to an area constraint. Equivalently these surfaces are critical points of the Geroch-Hawking mass. Thus our result has applications in the theory of general relativity.
In this article, the fractional variational iteration method is employed for computing the approximate analytical solutions of degenerate parabolic equations with fractional time derivative. The time-fractional derivatives are described by the use of a new approach, the so-called Jumarie modified Riemann-Liouville derivative, instead in the sense of Caputo. The approximate solutions of our model problem are calculated in the form of convergent series with easily computable components. Moreover, the numerical solution is compared with the exact solution and the quantitative estimate of accuracy is obtained. The results of the study reveal that the proposed method with modified fractional Riemann-Liouville derivatives is efficient, accurate, and convenient for solving the fractional partial differential equations in multi-dimensional spaces without using any linearization, perturbation or restrictive assumptions.
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t similar to s(-2) one component of the system is described for the most part by the inhomogeneous Mathieu equation while the other component represents pulsation of large amplitude. A Hamiltonian system is obtained which describes for the most part the behavior of the envelope in a special case. The analytic results agree with numerical simulations.