Hausdorff dimension of some groups acting on the binary tree

Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T. Abert and Virag showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0,1]. In this article we explicitly compute the Hausdorff dimension of the level-transitive spinal groups. We then show examples of 3-generated spinal groups which have transcendental Hausdroff dimension, and exhibit a construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof

Temperature response of ex-situ greenhouse gas emissions from tropical peatlands: Interactions between forest type and peat moisture conditions

Climate warming is likely to increase carbon dioxide (CO2) and methane (CH4) emissions from tropical wetlands by stimulating microbial activity, but the magnitude of temperature response of these CO2 and CH4 emissions, as well as variation in temperature response among forest types, is poorly understood. This limits the accuracy of predictions of future ecosystem feedbacks on the climate system, which is a serious knowledge gap as these tropical wetland ecosystems represent a very large source of greenhouse gas emissions (e.g. two-thirds of CH4 emissions from natural wetlands are estimated to be from tropical systems). In this study, we experimentally manipulated temperatures and moisture conditions in peat collected from different forest types in lowland neotropical peatlands in Panama and measured how this impacted ex-situ CO2 and CH4 emissions. The greatest temperature response was found for anaerobic CH4 production (Q10 = 6.8), and CH4 consumption (mesic conditions, Q10 = 2.7), while CO2 production showed a weaker temperature response (Q10 2 production was found under flooded oxic conditions. Net emissions of CO2 and CH4 were greatest from palm forest under all moisture treatments. Furthermore, the temperature response of CH4 emissions differed among dominant vegetation types with the strongest response at palm forest sites where fluxes increased from 42 ± 25 to 2166 ± 842 ng CH4 g−1 h−1 as temperatures were raised from 20 to 35 °C. We conclude that CH4 fluxes are likely to be more strongly impacted by higher temperatures than CO2 fluxes but that responses may differ substantially among forest types. Such differences in temperature response among forest types (e.g. palm vs evergreen broad leaved forest types) need to be considered when predicting ecosystem greenhouse gas responses under future climate change scenarios

Diverse Functions of Retinoic Acid in Brain Vascular Development

As neural structures grow in size and increase metabolic demand, the CNS vasculature undergoes extensive growth, remodeling, and maturation. Signals from neural tissue act on endothelial cells to stimulate blood vessel ingression, vessel patterning, and acquisition of mature brain vascular traits, most notably the blood–brain barrier. Using mouse genetic and in vitro approaches, we identified retinoic acid (RA) as an important regulator of brain vascular development via non-cell-autonomous and cell-autonomous regulation of endothelial WNT signaling. Our analysis of globally RA-deficient embryos (Rdh10 mutants) points to an important, non-cell-autonomous function for RA in the development of the vasculature in the neocortex. We demonstrate that Rdh10 mutants have severe defects in cerebrovascular development and that this phenotype correlates with near absence of endothelial WNT signaling, specifically in the cerebrovasculature, and substantially elevated expression of WNT inhibitors in the neocortex. We show that RA can suppress the expression of WNT inhibitors in neocortical progenitors. Analysis of vasculature in non-neocortical brain regions suggested that RA may have a separate, cell-autonomous function in brain endothelial cells to inhibit WNT signaling. Using both gain and loss of RA signaling approaches, we show that RA signaling in brain endothelial cells can inhibit WNT-β-catenin transcriptional activity and that this is required to moderate the expression of WNT target Sox17. From this, a model emerges in which RA acts upstream of the WNT pathway via non-cell-autonomous and cell-autonomous mechanisms to ensure the formation of an adequate and stable brain vascular plexus

Anterior implant restorations with a convex emergence profile increase the frequency of recession: 12-month results of a randomized controlled clinical trial

AIM To test whether the emergence profile (CONVEX or CONCAVE) of implant-supported crowns influences the mucosal margin stability up to 12 months after insertion of the final restoration. MATERIALS AND METHODS Forty-seven patients with a single implant in the anterior region were randomly allocated to one of three groups: (1) CONVEX (n = 15), implant provisional and an implant-supported crown both with a convex profile; (2) CONCAVE (n = 16), implant provisional and an implant-supported crown both with a concave profile; (3) CONTROL (n = 16), no provisional (healing abutment only) and an implant-supported crown. All patients were recalled at baseline, 6, and 12 months. The stability of mucosal margin along with clinical, aesthetic, and profilometric outcomes as well as time and costs were evaluated. To predict the presence of recession, multivariable logistic regressions were performed and linear models using generalized estimation equations were conducted for the different outcomes. RESULTS Forty-four patients were available at 12 months post-loading. The frequency of mucosal recession amounted to 64.3% in group CONVEX, 14.3% in group CONCAVE, and 31.4% in group CONTROL. Regression models revealed that a CONVEX profile was significantly associated with the presence of recessions (odds ratio: 12.6, 95% confidence interval: 1.82-88.48, p = .01) compared with the CONCAVE profile. Pink aesthetic scores amounted to 5.9 in group CONVEX, 6.2 in group CONCAVE, and 5.4 in group CONTROL, with no significant differences between the groups (p = .735). Groups CONVEX and CONCAVE increased the appointments and costs compared with the CONTROL group. CONCLUSIONS The use of implant-supported provisionals with a CONCAVE emergence profile results in a greater stability of the mucosal margin compared with a CONVEX profile up to 12 months of loading. This is accompanied, however, by increased time and costs compared with the absence of a provisional and may not necessarily enhance the aesthetic outcomes. TRIAL REGISTRATION German Clinical Trials Register; DRKS00009420

Restorative angle of zirconia restorations cemented on non-original titanium bases influences the initial marginal bone loss: 5-year results of a prospective cohort study

AIM: To assess radiographic, restorative, clinical and technical outcomes as well as patient satisfaction of directly veneered zirconia restorations cemented on non-original titanium bases over 5 years. MATERIAL AND METHODS: Twenty-four patients with a single missing tooth in the aesthetic zone were recruited. All patients received a two-piece implant with a screw-retained veneered zirconia restoration cemented extraorally on a titanium base abutment. Marginal bone levels (MBL), marginal bone changes, technical complications, patient satisfaction and clinical parameters including probing depth, bleeding on probing and plaque index were assessed at crown delivery (baseline), at 1 year (FU-1) and 5 years (FU-5) of follow-up. To investigate the relationship between restorative angle and MBL as well as marginal bone changes (bone loss/bone gain), correlation tests and linear regression models were carried out. RESULTS: Twenty-two patients were available for re-examination at 5 years. The mean MBL amounted to 0.54 ± 0.39 mm at baseline, and to 0.24 ± 0.35 at FU-5 (=bone gain) (p  .05). At distal sites, no correlations or associations between the restorative angle and MBL or marginal bone changes were found regardless of the time point. During the 5-year follow-up, 5 technical complications occurred, mainly within the first year and mostly chippings. All patients were entirely satisfied with their implant-supported restoration at 5 years. CONCLUSION: Within the limitations of the present study, the restorative angle of implant-supported crowns on non-original titanium bases might influence the initial marginal bone loss but without affecting their favourable long-term clinical performance. A restorative angle of <40° may limit the initial marginal bone loss at implant-supported crowns with titanium bases

On the state dependency of fast feedback processes in (palaeo) climate sensitivity

Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual climate model for interpretation. Applying a new method to account for background state dependency, we find $S^a=0.61\pm0.06$ K(Wm$^{-2}$)$^{-1}$ using the latest LGM temperature reconstruction and significantly lower climate sensitivity during glacial climates. Due to uncertainties in reconstructing the LGM temperature anomaly, $S^a$ is estimated in the range $S^a=0.55-0.95$ K(Wm$^{-2}$)$^{-1}$.Comment: submitted to Geophysical Research Letter