Large deviations for the local times of a random walk among random conductances in a growing box

We derive an annealed large deviation principle (LDP) for the normalised and rescaled local times of a continuous-time random walk among random conductances (RWRC) in a time-dependent, growing box in $\Z^d$. We work in the interesting case that the conductances are positive, but may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small conductance values and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution as well as the time-dependent size of the box. An interesting phase transition occurs if the thickness parameter of the conductance tails exceeds a certain threshold: for thicker tails, the random walk spreads out over the entire growing box, for thinner tails it stays confined to some bounded region. In fact, in the first case, the rate function turns out to be equal to the $p$-th power of the $p$-norm of the gradient of the square root for some $p\in(\frac {2d}{d+2},2)$. This extends the Donsker-Varadhan-G\"artner rate function for the local times of Brownian motion (with deterministic environment) from $p=2$ to these values. As corollaries of our LDP, we derive the logarithmic asymptotics of the non-exit probability of the RWRC from the growing box, and the Lifshitz tails of the generator of the RWRC, the randomised Laplace operator. To contrast with the annealed, not uniformly elliptic case, we also provide an LDP in the quenched setting for conductances that are bounded and bounded away from zero. The main tool here is a spectral homogenisation result, based on a quenched invariance principle for the RWRC.Comment: 32 page

Large deviations for the local times of a random walk among random conductances

We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $\Z^d$ in the spirit of Donsker-Varadhan \cite{DV75}. We work in the interesting case that the conductances may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small values of the conductances and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution. As an application, we identify the logarithmic asymptotics of the lower tails of the principal eigenvalue of the randomly perturbed negative Laplace operator in the domain.Comment: 12 page

Generischer Architekturansatz für Telemedizin Portale und verteilte Krankenakten

Dieser Aufsatz beschäftigt sich mit Softwarearchitekturen und Kriterien für deren längerfristige Verwendbarkeit als Basisansatz für die Entwicklung von verteilten Krankenakten und Telemedizin-Portalen. Im Vorfeld der Entwicklung eines verteilten Krankenaktensystems mit Portalfrontend am Klinikum der Universität Regensburg werden hierfür verschiedene Architekturansätze untersucht. Dabei soll ein Architekturprinzip gefunden werden, das unabhängig von Technologien und Standards die Entwicklung flexibler und gut integrierbarer verteilter Krankenaktensysteme ermöglicht. Nichtfunktionale Anforderungen der gesuchten Lösung sind Veränderbarkeit, Anpassbarkeit, Zuverlässigkeit, Erweiterbarkeit und Fehlerrobustheit. Das hier vorgestellte Konzept wurde während der Vorstudien zum Aufbau des Portalsystems entwickelt; bisherige Erfahrungen aus dem Betrieb des Portals stützen die dort getroffenen Annahmen. Als zentraler Anwendungsfall für die beiden genannten Systemtypen wird die gemeinsame Nutzung medizinischer Dokumente innerhalb einer stark heterogenen Systemlandschaft vorausgesetzt

The Shape of the Renormalized Trajectory in the Two-dimensional O(N) Non-linear Sigma Model

The renormalized trajectory in the multi-dimensional coupling parameter space of the two-dimensional O(3) non-linear sigma model is determined numerically under \linebreak $\delta$-function block spin transformations using two different Monte Carlo renormalization group techniques. The renormalized trajectory is compared with the straight line of the fixed point trajectory (fixed point action) which leaves the asymptotically free ultraviolet fixed point of the critical surface in the orthogonal direction. Our results show that the renormalized trajectory breaks away from the fixed point trajectory in a range of the correlation length around $\xi \approx 3$-$7$, flowing into the high temperature fixed point at $\xi=0$. The analytic large $N$ calculation of the renormalized trajectory is also presented in the coupling parameter space of the most general bilinear Hamiltonians. The renormalized trajectory in the large $N$ approximation exhibits a similar shape as in the $N=3$ case, with the sharp break occurring at a smaller correlation length of $\xi \approx 2$-$3$.Comment: 9 pages, compressed and uuencoded postscript file (compressed file is 434 Kbytes.) A reference is added with a minor modification of the text and fig.3

Successful Treatment of Early Relapsed High-Risk AML After Allogeneic Hematopoietic Stem Cell Transplantation With Biomodulatory Therapy

Early relapse of acute myeloid leukemia (AML) after allogeneic hematopoietic stem cell transplantation (allo-HSCT) is an often unsuccessful therapeutic challenge. Since treatment options are few and efficacy is low, new approaches such as de novo allo-HSCT, targeted therapies and biomodulatory drugs have been developed, albeit prognosis is very poor. In this manuscript we present an unusual case of a patient with high-risk AML with an unbalanced jumping translocation and FLT3-TKD (low) mutation who presented with early relapse (FLT3 negative) after allo-HSCT, refractory to one cycle of azacytidine and discontinuation of immunosuppression (IS). As salvage therapy, the patient received a biomodulatory therapy consisting of low-dose azacytidine 75 mg/day (given s.c. d1-7 of 28), pioglitazone 45 mg/day orally, and all-trans-retinoic acid (ATRA) 45 mg/m(2)/day orally achieving a complete remission after two cycles of therapy. Even after cessation of treatment after 5 cycles, the patient remained in complete remission with full chimerism in peripheral blood and bone marrow for another 7 months. In conclusion, we report about an unusual case of long-lasting complete remission of early relapsed high-risk AML after allo-HSCT treated with azacytidine, pioglitazone and ATRA after standard of care treatment with HMA and discontinuation of IS failed