Strong existence and uniqueness for stochastic differential equation with H{\"o}lder drift and degenerate noise

In this paper, we prove pathwise uniqueness for stochastic degenerate systems with a H{\"o}lder drift, for a H{\"o}lder exponent larger than the critical value 2/3. This work extends to the degenerate setting the earlier results obtained by Zvonkin, Veretennikov, Krylov and R{\"o}ckner from non-degenerate to degenerate cases. The existence of a threshold for the H{\"o}lder exponent in the degenerate case may be understood as the price to pay to balance the degeneracy of the noise. Our proof relies on regularization properties of the associated PDE, which is degenerate in the current framework and is based on a parametrix method

Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise

We consider two exit problems for the Korteweg-de Vries equation perturbed by an additive white in time and colored in space noise of amplitude a. The initial datum gives rise to a soliton when a=0. It has been proved recently that the solution remains in a neighborhood of a randomly modulated soliton for times at least of the order of a^{-2}. We prove exponential upper and lower bounds for the small noise limit of the probability that the exit time from a neighborhood of this randomly modulated soliton is less than T, of the same order in a and T. We obtain that the time scale is exactly the right one. We also study the similar probability for the exit from a neighborhood of the deterministic soliton solution. We are able to quantify the gain of eliminating the secular modes to better describe the persistence of the soliton

Extended-Linking Services: towards a Quality Web

A URL takes requesters from a citation to a destination… provided, of course, the URL is still valid. The current chaotic web is wonderful in its way. However, within this chaotic web, we believe there is a need for a high-quality web of vetted information. The emerging OpenURL standard is the cornerstone of a worldwide web with high-quality links that feature properties such as: •Persistence: Increase the probable lifetime of citations. •Multiplicity: Produce a menu of targeted services for each citation. •Context-Sensitivity: Resolve a citation in a manner appropriate to the user and to the context. To encourage the development of extended-linking services, NISO formed a committee to develop a standard OpenURL syntax. Our immediate goal is to serve the scholarly-information community immediately. However, the OpenURL technique is widely applicable, and we expect to serve many other information communities

AKI patients have worse long-term outcomes, especially in the immediate post-ICU period

Acute kidney injury (AKI) is associated with worse outcome in the acute phase of acute illness but also in the chronic phase. In a large Danish study in this issue of Critical Care, 1-year mortality was higher in patients with AKI than in patients without AKI. Mortality was most important during the first 50 days after admission to the intensive c are unit (ICU), whereas after 2 months the survival curves of patients with AKI and those of patients without AKI were similar. The reasons for this observation are not clear, but protracted critical illness and fragility after acute critical illness probably play important roles. Because we see more and more of these patients, they should be the focus of ICU research. Consequently, ICU and post-ICU care for these patients requires focus and a more integrated approach to the specific problems of these survivors of acute critical illness

To Bin or Not To Bin: Decorrelating the Cosmic Equation of State

The physics behind the acceleration of the cosmic expansion can be elucidated through comparison of the predictions of dark energy equations of state to observational data. In seeking to optimize this, we investigate the advantages and disadvantages of using principal component analysis, uncorrelated bandpowers, and the equation of state within redshift bins. We demonstrate that no one technique is a panacea, with tension between clear physical interpretation from localization and from decorrelated errors, as well as model dependence and form dependence. Specific lessons include the critical role of proper treatment of the high redshift expansion history and the lack of a unique, well defined signal-to-noise or figure of merit.Comment: 26 pages, 28 figure

Calibrating Dark Energy

Exploring the diversity of dark energy dynamics, we discover a calibration relation, a uniform stretching of the amplitude of the equation of state time variation with scale factor. This defines homogeneous families of dark energy physics. The calibration factor has a close relation to the standard time variation parameter w_a, and we show that the new, calibrated w_a describes observables, i.e. distance and Hubble parameter as a function of redshift, typically to an accuracy level of 10^{-3}. We discuss implications for figures of merit for dark energy science programs.Comment: 9 pages, 10 figure

Alternating-Direction Line-Relaxation Methods on Multicomputers

We study the multicom.puter performance of a three-dimensional Navier–Stokes solver based on alternating-direction line-relaxation methods. We compare several multicomputer implementations, each of which combines a particular line-relaxation method and a particular distributed block-tridiagonal solver. In our experiments, the problem size was determined by resolution requirements of the application. As a result, the granularity of the computations of our study is finer than is customary in the performance analysis of concurrent block-tridiagonal solvers. Our best results were obtained with a modified half-Gauss–Seidel line-relaxation method implemented by means of a new iterative block-tridiagonal solver that is developed here. Most computations were performed on the Intel Touchstone Delta, but we also used the Intel Paragon XP/S, the Parsytec SC-256, and the Fujitsu S-600 for comparison