The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations

We consider a Markov chain on the space of (countable) partitions of the interval [0,1], obtained first by size biased sampling twice (allowing repetitions) and then merging the parts (if the sampled parts are distinct) or splitting the part uniformly (if the same part was sampled twice). We prove a conjecture of Vershik stating that the Poisson-Dirichlet law with parameter theta=1 is the unique invariant distribution for this Markov chain. Our proof uses a combination of probabilistic, combinatoric, and representation-theoretic arguments.Comment: To appear in Annals Probab. 6 figures Only change in new version is addition of proof (at end of article) that the state (1,0,0,...) is transien

Comparison of Intravitreal Bevacizumab Upload Followed by a Dexamethasone Implant versus Dexamethasone Implant Monotherapy for Retinal Vein Occlusion with Macular Edema

Purpose: To compare the efficacy and safety of three intravitreal bevacizumab upload injections followed by a dexamethasone implant versus dexamethasone implant monotherapy in eyes with macular edema due to retinal vein occlusion. Methods: Sixty-four eyes of 64 patients were included in this prospective, consecutive, nonrandomized case series: group 1 consisted of 38 patients (22 with central retinal vein occlusion, CRVO, 16 with branch retinal vein occlusion, BRVO) treated using a dexamethasone implant (Ozurdex) alone; group 2 consisted of 26 patients (14 CRVO, 12 BRVO) treated with three consecutive intravitreal bevacizumab injections at monthly intervals followed by a dexamethasone implant. In case of recurrence, both cohorts received further dexamethasone implants. Preoperatively and monthly best corrected visual acuity (BCVA, ETDRS), central retinal thickness (Spectralis-OCT), intraocular pressure, and wide-angle fundus photodocumentation (Optomap) were performed. The primary clinical endpoint was BCVA at 6 months after initiation of therapy. Secondary endpoints were central retinal thickness and safety of the therapy applied. Results: In group 1, an increase in BCVA of 2.5 (+/- 1.6) letters in the CRVO and of 13.0 (+/- 3.2) letters in BRVO patients was seen after 6 months, in group 2 of 5.9 (+/- 0.4) letters (CRVO) and 3.8 (+/- 2.4) letters (BRVO), which was not statistically significant. When comparing the two treatment groups with respect to the type of vein occlusion, there was a significant advantage for BRVO patients for the dexamethasone implant monotherapy (BRVO patients in group 1, p = 0.005). Central retinal thickness showed a significant reduction after 6 months only in patients of group 1, both for CRVO (p = 0.01) and BRVO (p = 0.003). First recurrence after the first dexamethasone implant injection occurred after 3.8 months (mean) in CRVO and 3.5 months in BRVO patients (group 1), versus 3.2 and 3.7 months, respectively, in group 2. In group 1, 63.6% with CRVO and 50% with BRVO showed an increased intraocular pressure after treatment; in group 2, 57.1% with CRVO and 50.0% with BRVO, respectively. Conclusion: In CRVO, there was no difference between the two treatment strategies investigated. However, in BRVO, dexamethasone implant monotherapy was associated with better functional outcome. Copyright (C) 2012 S. Karger AG, Base

Introduction: enquiries into the history of geology

The International Commission on the History of Geological Sciences was founded in 1967 at a meeting in Yerevan, Armenia. After an initial attempt to form an association of historians of geology at the International Geological Congress (IGC) in Copenhagen in 1960, a fresh proposal was approved at the following IGC in New Delhi, in 1964. Steps were then taken that led to the formal establishment of INHIGEO at Yerevan three years later

The Necessity for a Time Local Dimension in Systems with Time Varying Attractors

We show that a simple non-linear system of ordinary differential equations may possess a time varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non-stationary attractors.Comment: 13 Postscript pages, 12 Postscript figures (figures 3b and 4 by request from Y. Ashkenazy: [email protected]

Inhibitor of Apoptosis Proteins as Novel Targets in Inflammatory Processes

Objective: Inhibitor of apoptosis proteins (IAPs), such as X-linked or cellular IAP 1/2 (XIAP, cIAP1/2), are important regulators of apoptosis. IAP antagonists are currently under clinical investigation as anticancer agents. Interestingly, IAPs participate in the inflammation-associated TNF receptor signaling complex and regulate NFκB signaling. This raises the question about the role of IAPs in inflammation. Here, we investigated the anti-inflammatory potential of IAP inhibitors and the role of IAPs in inflammatory processes of endothelial cells. Methods and Results: In mice, the small molecule IAP antagonist A-4.10099.1 (ABT) suppressed antigen-induced arthritis, leukocyte infiltration in concanavalin A-evoked liver injury, and leukocyte transmigration in the TNFα-activated cremaster muscle. In vitro, we observed an attenuation of leukocyte– endothelial cell interaction by downregulation of the intercellular adhesion molecule-1. ABT did not impair NFκB signaling but decreased the TNFα-induced activation of the TGF-β–activated kinase 1, p38, and c-Jun N-terminal kinase. These effects are based on the proteasomal degradation of cIAP1/2 accompanied by an altered ratio of the levels of membrane-localized TNF receptor-associated factors 2 and 5. Conclusion: Our results reveal IAP antagonism as a profound anti-inflammatory principle in vivo and highlight IAPs as important regulators of inflammatory processes in endothelial cells