The Topology of Parabolic Character Varieties of Free Groups

Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe explicit examples relating X to relative character varieties.Comment: 16 pages, version 2 includes minor revisions and some modified proofs, accepted for publication in Geometriae Dedicat

Warped Riemannian metrics for location-scale models

The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry. Precisely, the paper features a new theorem, which states that the Rao-Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action of some Lie group. This theorem is a valuable tool in finding the expression of the Rao-Fisher information metric of location-scale models defined on high-dimensional Riemannian manifolds. Indeed, a warped Riemannian metric is fully determined by only two functions of a single variable, irrespective of the dimension of the underlying Riemannian manifold. Starting from this theorem, several original contributions are made. The expression of the Rao-Fisher information metric of the Riemannian Gaussian model is provided, for the first time in the literature. A generalised definition of the Mahalanobis distance is introduced, which is applicable to any location-scale model defined on a Riemannian manifold. The solution of the geodesic equation is obtained, for any Rao-Fisher information metric defined in terms of warped Riemannian metrics. Finally, using a mixture of analytical and numerical computations, it is shown that the parameter space of the von Mises-Fisher model of $n$-dimensional directional data, when equipped with its Rao-Fisher information metric, becomes a Hadamard manifold, a simply-connected complete Riemannian manifold of negative sectional curvature, for $n = 2,\ldots,8$. Hopefully, in upcoming work, this will be proved for any value of $n$.Comment: first version, before submissio

Singularities and Topology of Meromorphic Functions

We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.Comment: 21 pages, 1 figur

Diabetes MILES – The Netherlands: rationale, design and sample characteristics of a national survey examining the psychosocial aspects of living with diabetes in Dutch adults

Background : As the number of people with diabetes is increasing rapidly worldwide, a more thorough understanding of the psychosocial aspects of living with this condition has become an important health care priority. While our knowledge has grown substantially over the past two decades with respect to the physical, emotional and social difficulties that people with diabetes may encounter, many important issues remain to be elucidated. Under the umbrella of the Diabetes MILES (Management and Impact for Long-term Empowerment and Success) Study International Collaborative, Diabetes MILES &ndash; The Netherlands aims to examine how Dutch adults with diabetes manage their condition and how it affects their lives. Topics of special interest in Diabetes MILES - The Netherlands include subtypes of depression, Type D personality, mindfulness, sleep and sexual functioning. Methods/design : Diabetes MILES &ndash; The Netherlands was designed as a national online observational study among adults with diabetes. In addition to a main set of self-report measures, the survey consisted of five complementary modules to which participants were allocated randomly. From September to October 2011, a total of 3,960 individuals with diabetes (40% type 1, 53% type 2) completed the battery of questionnaires covering a broad range of topics, including general health, self-management, emotional well-being and contact with health care providers. People with self-reported type 1 diabetes (specifically those on insulin pump therapy) were over-represented, as were those using insulin among respondents with self-reported type 2 diabetes. People from ethnic minorities were under-represented. The sex distribution was fairly equal in the total sample, participants spanned a broad age range (19&ndash;90 years), and diabetes duration ranged from recent diagnosis to living with the condition for over fifty years. Discussion : The Diabetes MILES Study enables detailed investigation of the psychosocial aspects of living with diabetes and an opportunity to put these findings in an international context. With several papers planned resulting from a pooled Australian-Dutch dataset and data collections planned in other countries, the Diabetes MILES Study International Collaborative will contribute substantially to identifying potentially unmet needs of those living with diabetes and to inform clinical research and care across the globe. <br /

Measurement of prompt J/ψ pair production in pp collisions at √s = 7 Tev

Peer reviewe

Observation of the diphoton decay of the Higgs boson and measurement of its properties

Peer reviewe

Measurement of top quark–antiquark pair production in association with a W or Z boson in pp collisions at √s=8 TeV

Peer reviewe