Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Ontogenetic changes in leaf traits of tropical rainforest trees differing in juvenile light requirement

Relationships between leaf traits and the gap dependence for regeneration, and ontogenetic changes therein, were investigated in juvenile and adult tropical rainforest tree species. The juveniles of the 17 species included in the study were grown in high light, similar to the exposed crowns of the adult trees. The traits were structural, biomechanical, chemical and photosynthetic. With increasing species gap dependence, leaf mass per area (LMA) decreased only slightly in juveniles and remained constant in adults, whereas punch strength together with tissue density decreased, and photosynthetic capacity and chlorophyll increased. Contrary to what has been mostly found in evergreen tropical rainforest, the trade-off between investment in longevity and in productivity was evident at an essentially constant LMA. Of the traits pertaining to the chloroplast level, photosynthetic capacity per unit chlorophyll increased with gap dependence, but the chlorophyll a/b ratio showed no relationship. Adults had a twofold higher LMA, but leaf strength was on average only about 50% larger. Leaf tissue density, and chlorophyll and leaf N per area were also higher, whereas chlorophyll and leaf N per unit dry mass were lower. Ranking of the species, relationships between traits and with the gap dependence of the species were similar for juveniles and adults. However, the magnitudes of most ontogenetic changes were not clearly related to a species’ gap dependence. The adaptive value of the leaf traits for juveniles and adults is discussed

The optimization of footwear choices in the management of knee osteoarthritis

Background: An estimated 4.71 million people aged 45 and over have sought treatment for knee osteoarthritis (OA) in the UK, with this number predicted to grow to 6.5 million people by 2020. Structural changes of knee OA are the most common cause of disability in the UK; symptoms include pain, stiffness, crepitus, swelling and giving way, increasing the risk factor for falls. Medial compartment osteoarthritis (MCOA) has been found to be the most common form of OA and dynamic joint loading has been implicated in disease progression. It has been postulated that various load-bearing conditions alter kinematics and kinetic load and this has the potential to unevenly distribute load across articular cartilage surfaces. NICE guidelines have stipulated that conservative treatment methods, such as footwear for long-term self-management of knee osteoarthritis are a priority for research due to the prevalence of OA and the growing population. The objective of therapeutic footwear is to distribute load evenly across the knee joint by reducing the peak external knee adduction moment (EKAM) and knee adduction angular impulse (KAAI) by manipulating the vertical ground reaction force vector laterally to the knee joint centre and preventing exaggerated adduction of the tibia. The purpose of this review was to explore the literature in relation to footwear that have specific design features, aimed at providing symptom relief and reducing EKAM and KAAI in individuals living with MCOA. Additionally taking in consideration the needs, expectations and perspectives of the at risk population. Methods: Systematic searches were carried out in July 2016, using the EBSCOhost research database (SPORTDiscus, Medline, CINAHL and Academic search premier), Pubmed and Web of Science. Critical appraisal was performed using the validated Downs and Black appraisal tool. Results: Fifteen articles satisfied the inclusion criteria. Overall, articles appraised were scored fair to moderate methodological quality. All footwear revealed variable reductions of first peak EKAM and KAAI when compared to control shoes that were selected due to their stable and supportive nature. All research that compared shod conditions to barefoot walking found that shoes increased first and second peak EKAM and KAAI. Minimalist footwear reflected the kinetic and kinematic components of barefoot walking. Natural movement patterns and increased lower limb muscular activity are evidenced to be biomechanically and symptomatically beneficial. Conclusion: Biomechanical adaptations exhibited through use of conventional and offloading shoes increase EKAM and KAAI significantly when compared to the barefoot walking condition, this significantly increases the risk of disease progression. Minimalist footwear closely mimics the significantly lower knee loading and kinematic characteristics of barefoot walking. A therapeutic effect could be induced by providing a less supportive platform, thereby facilitating improved neuromuscular control, joint stability and alleviating abnormal joint loading

The Impact of Customer Community Participation on Customer Behaviors: An Empirical Investigation

Many firms increasingly offer community venues to their customers to facilitate social interactions amongst them. Prior studies have shown that community participants have high engagement and loyalty toward the firm and provide useful feedback and referrals. However, it is not clear whether community participants are the firm's "fans" to begin with and self-select themselves into the community, or whether community participation leads to increased relational customer behaviors. In the current research, we employ data from a field experiment to help answer this question. The data come from a year-long study conducted by eBay Germany, and they reveal that a simple e-mail invitation significantly increased customer participation in the firm's community. Results also show that community participation had mixed effects on customers' likelihoods of participating in buying and selling behaviors. Community participation did not translate into increased behaviors, as would be commonly expected. Although there is no impact of participation on the number of bids placed or the revenue earned, there is a negative impact of participation on the number of listings and the amount spent. Together, these results suggest that the community participants become more selective and efficient sellers, and they also become more conservative in their spending on the items for which they bid. The results also show that customer community marketing programs may be targeted to a broader set of the firm's customers than just the fans.customer community, online social interactions, customer relationship management, hierarchical bayes, MCMC, multivariate Tobit