Aims. We study degeneracies between cosmological parameters and measurement errors from cosmic shear surveys. We simulate realistic survey topologies with non-uniform sky coverage, and quantify the effect of survey geometry, depth and noise from intrinsic galaxy ellipticities on the parameter errors. This analysis allows us to optimise the survey geometry. Methods. We carry out a principal comp...

Classical information geometry prescribes, on the parametric family of probability functions Mθ : (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint actions; and (iii) a family of (non-symmetric) divergence functions (α-divergence) defined on Mθ ×Mθ...

Almost rotation minimizing parametrization of the canal surface is given. The basic building block of our approach is the curve approximation scheme that enables us to construct a curve, called the parameter curve, on the canal surface that produces, when projected and rescaled, an almost parallel normal vector field on the spine curve. Its construction relies on our earlier methods and results...

An effective property of a composite material consisting of inclusions within a host matrix depends on the geometry and connectedness of the inclusions. This dependence may be quite strong if the constituents have highly contrasting properties. Here we consider the inverse problem of using effective property data to obtain information on the geometry of the microstructure. While previous work h...

The geometry of rivers has been characterized in terms of downstream and at-a-station hydraulic geometry, based on individual cross sections. Such analyses do not, however, provide insight as to how these cross sections are connected. We generalize the concept of hydraulic geometry, using data on bathymetry from four reaches of meandering rivers that include at least five bends. We quantify con...

In this paper, we study the geometry induced by Fisher-Rao metric on parameter space of Dirichlet distributions. We show that is geodesically complete and has everywhere negative sectional curvature. An important consequence curvature for applications Fr{\'e}chet mean a set distributions uniquely defined in geometry.