Motivated by recent developments on calculus in metric measure spaces (X, d,m), we prove a general duality principle between Fuglede’s notion [15] of p-modulus for families of finite Borel measures in (X, d) and probability measures with barycenter in Lq(X,m), with q dual exponent of p ∈ (1,∞). We apply this general duality principle to study null sets for families of parametric and non-paramet...

We develop a family of infinite-dimensional (i.e. non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class Ck b with respect to appropriate reference measures. The case k = ∞, in which the manifolds are modelled on Fréchet spaces, is included. The manifolds admit the Fisher-Rao metric and the dually flat geometry of Amari...

Objectives. To build a 3D parametric model to detect shape and volume of dental roots, from a panoramic radiograph (PAN) of the patient. Materials and Methods. A PAN and a cone beam computed tomography (CBCT) of a patient were acquired. For each tooth, various parameters were considered (coronal and root lengths and widths): these were measured from the CBCT and from the PAN. Measures were comp...

With the advent of high frequency data, research has been instigated into the intra-day and integrated volatility, measured through e.g. realised volatility. Such measures may be contaminated by microstructure effects and jumps, leading to the development of alternative nonparametric estimators using quadratic variation measures. Instead of using such model-agnostic, non-parametric measures, th...

In this paper we consider masonry bodies undergoing loads that can be represented by vector valued measures, and prove a result which is an appropriate formulation to this context of the static theorem of the limit analysis. As applications, we study the equilibrium of panels that are subjected both to distributed loads and concentrated forces, and determine equilibrated tensor valued measures....