Entry and Return times distribution

This is a review article on the distributions of entry and return times in dynamical systems which discusses recent results for systems of positive entropy.Comment: To appear in "Dynamical Systems: An International Journal dedicated to the Statistical Properties of Dynamical Systems

Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the radius. In order to get those uniform rates of convergence the balls centres have to avoid a set whose size is estimated to be of similar order. This result can be applied to non-uniformly hyperbolic maps and to any invariant measure that satisfies a weak regularity condition. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.Comment: 28 page

Gradient Representations and Affine Structures in AE(n)

We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.Comment: 43 page

Convergence rates of general regularization methods for statistical inverse problems and applications

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators are simpler to compute, but still involve the inversion of an operator and achieve minimax rates only in restricted smoothness classes. In this paper we introduce a unifying technique to study the mean square error of a large class of regularization methods (spectral methods) including the aforementioned estimators as well as many iterative methods, such as í-methods and the Landweber iteration. The latter estimators converge at the same rate as spectral cut-off, but only require matrixvector products. Our results are applied to various problems, in particular we obtain precise convergence rates for satellite gradiometry, L2-boosting, and errors in variable problems. --Statistical inverse problems,iterative regularization methods,Tikhonov regularization,nonparametric regression,minimax convergence rates,satellite gradiometry,Hilbert scales,boosting,errors in variable

Einsatz von gecufften Endotrachealtuben bei Kindern in der Notfall- und Rettungsmedizin

Zusammenfassung: Moderne Pädiatrietuben mit Cuff kommen in der Kinderanästhesie und Kinderintensivmedizin vermehrt zur Anwendung. Hohe Treffsicherheit bei der Tubusgrößenwahl sowie die zuverlässige Abdichtung des Atemwegssystems ohne den Einsatz übergroßer Tuben sind entscheidende Vorteile gecuffter Tuben auch bei Säuglingen und kleinen Kindern in der Notfall- und Rettungsmedizin. Für einen sicheren Einsatz gecuffter Tuben in dieser Altersgruppe ist die Auswahl eines Pädiatrietubus mit korrekt platziertem Hochvolumen-Niederdruck-Cuff und Intubationstiefenmarkierung sowie eine geprüfte Tubusgrößenauswahlliste die Vorraussetzung. Die Überprüfung des Tubus auf eine Luftleckage nach der Intubation bei noch entleertem Cuff, das Füllen des Cuffs unter Cuffdruckkontrolle sowie die Cuffdruckbegrenzung auf maximal 20cmH2O erlauben den sicheren Einsatz von gecufften Tuben bei Säuglingen und Kindern. Fehlen gute Kindertuben mit Cuff, Altersgrößenauswahlliste und Cuffmanometer, so dürfen gecuffte Tuben bei Säuglingen und Kindern in der Rettungs- und Notfallmedizin nicht eingesetzt werden. Dann sollten weiterhin ungecuffte Tuben zum Einsatz gelange

Self-diffusion of non-interacting hard spheres in particle gels

International audienceDifferent kinds of particle gels were simulated using a process of random aggregation of hard spheres. The mean square displacement of Brownian spherical tracer particles through these rigid gels was monitored and the average diffusion coefficient, normalized with the free diffusion coefficient (D), was obtained. For each gel structure the effect of the gel volume fraction (φ) and size ratio of the tracer (d) on the relative diffusion coefficient was investigated systematically. The volume fraction that is accessible to the tracers (φa) was determined in eachcase. D was found to be approximately the same if φa was the same, independent of φ, d and the gel structure. However a different behaviour is found if the tracers can penetrate the strands of the gel. A state diagram of d versus φ is given that shows the critical values (dc, φc) at whichall tracers become trapped. Different values are found for different gel structures. The dependence of D on φ/φc is independent of d, while the dependence of D on d/dc is independent of φ