Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come

Phase Behavior of Aqueous Na-K-Mg-Ca-CI-NO3 Mixtures: Isopiestic Measurements and Thermodynamic Modeling

A comprehensive model has been established for calculating thermodynamic properties of multicomponent aqueous systems containing the Na{sup +}, K{sup +}, Mg{sup 2+}, Ca{sup 2+}, Cl{sup -}, and NO{sub 3}{sup -} ions. The thermodynamic framework is based on a previously developed model for mixed-solvent electrolyte solutions. The framework has been designed to reproduce the properties of salt solutions at temperatures ranging from the freezing point to 300 C and concentrations ranging from infinite dilution to the fused salt limit. The model has been parameterized using a combination of an extensive literature database and new isopiestic measurements for thirteen salt mixtures at 140 C. The measurements have been performed using Oak Ridge National Laboratory's (ORNL) previously designed gravimetric isopiestic apparatus, which makes it possible to detect solid phase precipitation. Water activities are reported for mixtures with a fixed ratio of salts as a function of the total apparent salt mole fraction. The isopiestic measurements reported here simultaneously reflect two fundamental properties of the system, i.e., the activity of water as a function of solution concentration and the occurrence of solid-liquid transitions. The thermodynamic model accurately reproduces the new isopiestic data as well as literature data for binary, ternary and higher-order subsystems. Because of its high accuracy in calculating vapor-liquid and solid-liquid equilibria, the model is suitable for studying deliquescence behavior of multicomponent salt systems

Osteogenic differentiation of mesenchymal stem cells is regulated by osteocyte and osteoblast cells in a simplified bone niche

Mesenchymal stem cells (MSCs) within their native environment of the stem cell niche in bone receive biochemical stimuli from surrounding cells. These stimuli likely influence how MSCs differentiate to become bone precursors. The ability of MSCs to undergo osteogenic differentiation is well established in vitro; however, the role of the natural cues from bone\u27s regulatory cells, osteocytes and osteoblasts in regulating the osteogenic differentiation of MSCs in vivo are unclear. In this study we delineate the role of biochemical signalling from osteocytes and osteoblasts, using conditioned media and co-culture experiments, to understand how they direct osteogenic differentiation of MSCs. Furthermore, the synergistic relationship between osteocytes and osteoblasts is examined by transwell co-culturing of MSCs with both simultaneously. Osteogenic differentiation of MSCs was quantified by monitoring alkaline phosphatase (ALP) activity, calcium deposition and cell number. Intracellular ALP was found to peak earlier and there was greater calcium deposition when MSCs were co-cultured with osteocytes rather than osteoblasts, suggesting that osteocytes are more influential than osteoblasts in stimulating osteogenesis in MSCs. Osteoblasts initially stimulated an increase in the number of MSCs, but ultimately regulated MSC differentiation down the same pathway. Our novel co-culture system confirmed a synergistic relationship between osteocytes and osteoblasts in producing biochemical signals to stimulate the osteogenic differentiation of MSCs. This study provides important insights into the mechanisms at work within the native stem cell niche to stimulate osteogenic differentiation and outlines a possible role for the use of co-culture or conditioned media methodologies for tissue engineering applications.The authors would like to acknowledge funding from the Irish Research Council for Science, Engineering and Technology, under the EMBARK program (E. Birmingham) and the Science Foundation Ireland E.T.S. Walton program 07/W.I./B1806 (G.L. Niebur)