Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

How do we get there? Effects of cognitive aging on route memory

© 2017 The Author(s) Research into the effects of cognitive aging on route navigation usually focuses on differences in learning performance. In contrast, we investigated age-related differences in route knowledge after successful route learning. One young and two groups of older adults categorized using different cut-off scores on the Montreal Cognitive Assessment (MoCA), were trained until they could correctly recall short routes. During the test phase, they were asked to recall the sequence in which landmarks were encountered (Landmark Sequence Task), the sequence of turns (Direction Sequence Task), the direction of turn at each landmark (Landmark Direction Task), and to identify the learned routes from a map perspective (Perspective Taking Task). Comparing the young participant group with the older group that scored high on the MoCA, we found effects of typical aging in learning performance and in the Direction Sequence Task. Comparing the two older groups, we found effects of early signs of atypical aging in the Landmark Direction and the Perspective Taking Tasks. We found no differences between groups in the Landmark Sequence Task. Given that participants were able to recall routes after training, these results suggest that typical and early signs of atypical aging result in differential memory deficits for aspects of route knowledge

Depleted dissolved organic carbon and distinct bacterial communities in the water column of a rapid-flushing coral reef ecosystem

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in The ISME Journal 5 (2011): 1374–1387, doi:10.1038/ismej.2011.12.Coral reefs are highly productive ecosystems bathed in unproductive, low-nutrient oceanic waters, where microbially-dominated food webs are supported largely by bacterioplankton recycling of dissolved compounds. Despite evidence that benthic reef organisms efficiently scavenge particulate organic matter and inorganic nutrients from advected oceanic waters, our understanding of the role of bacterioplankton and dissolved organic matter in the interaction between reefs and the surrounding ocean remains limited. Here we present the results of a four-year study conducted in a well-characterized coral reef ecosystem (Paopao Bay, Moorea, French Polynesia) where changes in bacterioplankton abundance and dissolved organic carbon (DOC) concentrations were quantified and bacterial community structure variation was examined along spatial gradients of the reef:ocean interface. Our results illustrate that the reef is consistently depleted in concentrations of both DOC and bacterioplankton relative to offshore waters (averaging 79 µmol L-1 DOC and 5.5 X 108 cells L-1 offshore and 68 µmol L-1 DOC and 3.1 X 108 cells L-1 over the reef, respectively) across a four year time period. In addition, using a suite of culture-independent measures of bacterial community structure, we found consistent differentiation of reef bacterioplankton communities from those offshore or in a nearby embayment across all taxonomic levels. Reef habitats were enriched in Gamma-, Delta-, and Beta-proteobacteria, Bacteriodetes, Actinobacteria and Firmicutes. Specific bacterial phylotypes, including members of the SAR11, SAR116, Flavobacteria, and Synechococcus clades, exhibited clear gradients in relative abundance among nearshore habitats. Our observations indicate that this reef system removes oceanic DOC and exerts selective pressures on bacterioplankton community structure on timescales approximating reef water residence times, observations which are notable both because fringing reefs do not exhibit long residence times (unlike those characteristic of atoll lagoons) and because oceanic DOC is generally recalcitrant to degradation by ambient microbial assemblages. Our findings thus have interesting implications for the role of oceanic DOM and bacterioplankton in the ecology and metabolism of reef ecosystems.This project was supported by the US National Science Foundation Moorea Coral Reef Long Term Ecological Research project (NSF OCE-0417412) through minigrants to CAC and NSF OCE-0927411 to CAC as well as the MIRADA-LTERs program (NSF DEB-0717390 to LAZ)

Phenotypic and functional analysis of lymphocytes infiltrating osteolytic tumors: use as a possible therapeutic approach of osteosarcoma

BACKGROUND: Osteosarcoma is the most common type of primary bone tumor. The use of aggressive chemotherapy has drastically improved the prognosis of the patients with non-metastatic osteosarcomas, however the prognosis of the patients with metastasis is still very poor. Then, new and more effective treatments for curing osteosarcoma, such as immunotherapy are needed. Tumor-infiltrating lymphocytes (TIL) have been involved in the control of tumor development and already assessed with success for the treatment of several cancers including melanoma. While TIL represent a fascinating therapeutic approach in numerous malignant pathologies, there is few report concerning adult bone-associated tumors including osteosarcoma. METHODS: Human TIL were isolated and characterized (phenotype, lytic activity) from twenty-seven patients with bone-associated tumors (osteosarcoma, Ewing's sarcoma, giant cell tumor, chondrosarcoma, plasmocytoma and bone metastases). Similar experiments were performed using rat osteosarcoma model. RESULTS: While TIL with a main CD4(+ )profile were easily isolated from most of the tumor samples, only TIL extracted from osteosarcoma were cytotoxic against allogeneic tumor cells. In all cases, TIL lytic activity was significantly higher compared to autologous peripheral blood leukocytes. Similar data were observed in rat osteosarcoma model where TIL were characterized by a main CD4(+ )profile and high lytic activity against allogeneic and autologous tumor cells. Moreover, rat TIL expansion was not accompanied by refractoriness to further activation stimulus mainly by tumor antigens. CONCLUSION: These results demonstrated that TIL therapy could be a very efficient strategy for the treatment of adult osteosarcoma