Entropic Ricci curvature bounds for discrete interacting systems

We develop a new and systematic method for proving entropic Ricci curvature lower bounds for Markov chains on discrete sets. Using different methods, such bounds have recently been obtained in several examples (e.g., 1-dimensional birth and death chains, product chains, Bernoulli-Laplace models, and random transposition models). However, a general method to obtain discrete Ricci bounds had been lacking. Our method covers all of the examples above. In addition, we obtain new Ricci curvature bounds for zero-range processes on the complete graph. The method is inspired by recent work of Caputo, Dai Pra and Posta on discrete functional inequalities.Comment: Published at http://dx.doi.org/10.1214/15-AAP1133 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

An axiomatic approach to default risk and model uncertainty in rating systems

In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step, we turn our focus on default risk measures, which are given as worst-case PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of capital requirements through risk-weighted assets (RWAs), as demanded by the Capital Requirement Regulation (CRR). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets.Comment: References have been updated, typos have been corrected, final version to appear in Journal of Mathematical Economic

A representation theorem for end spaces of infinite graphs

End spaces of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's for infinite groups. A long-standing quest in infinite graph theory with a rich body of literature seeks to describe the possible end structures of graphs by a set of low-complexity representatives. In this paper we present a solution to this fifty-year-old problem by showing that every end space is homeomorphic to the end space of some (uniform graph on a) special order tree.Comment: 23 pages. V2 adds a moreover-part to Theorem 3.

Bilingualism, Multilingualism, Globalization and Superdiversity:Toward Sociolinguistic Repertoires

A survey of developments in research on sociolinguistic superdiversity, emphasizing the increased relevance of repertoires as focus of research

Designing wheelchair-based movement games

People using wheelchairs have access to fewer sports and other physically stimulating leisure activities than nondisabled persons, and often lead sedentary lifestyles that negatively influence their health. While motion- based video games have demonstrated great potential of encouraging physical activity among nondisabled players, the accessibility of motion-based games is limited for persons with mobility disabilities, thus also limiting access to the potential health benefits of playing these games. In our work, we address this issue through the design of wheelchair-accessible motion-based game controls. We present KINECTWheels, a toolkit designed to integrate wheelchair movements into motion-based games. Building on the toolkit, we developed Cupcake Heaven, a wheelchair-based video game designed for older adults using wheelchairs, and we created Wheelchair Revolution, a motion-based dance game that is accessible to both persons using wheelchairs and nondisabled players. Evaluation results show that KINECTWheels can be applied to make motion-based games wheelchair-accessible, and that wheelchair-based games engage broad audiences in physically stimulating play. Through the application of the wheelchair as an enabling technology in games, our work has the potential of encouraging players of all ages to develop a positive relationship with their wheelchair