Related papers: On problematic case of product approximation in Ba…
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and…
Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of…
In this paper, we consider a long-wave equivalent medium to a finely parallel-layered inhomogeneous medium, obtained using the Backus average. Following the work of Postma and Backus, we show explicitly the derivations of the conditions to…
The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by…
Materials with negative Poisson's ratio, also known as auxetic materials, display exotic properties such as expansion in all directions under uni-axial tension. For their unique properties, these materials find a broad range of applications…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…
Microstructural models of soft tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they…
The lower bound usually cited for Poisson's ratio {\nu} is -1, derived from the relationship between {\nu} and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound…
We study the complexity of two closely related learning problems, one quantum and one classical. In the quantum setting, we consider agnostic tomography for the natural class of product mixed states. Given $N$ copies of an $n$-qubit state…
In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable.…
Metamaterials can enable unique mechanical properties based on their geometry rather than their chemical composition. Such properties can go beyond what is possible using conventional materials. Most of the existing literature consider…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…
This paper considers the posterior contraction of non-parametric Bayesian inference on non-homogeneous Poisson processes. We consider the quality of inference on a rate function $\lambda$, given non-identically distributed realisations,…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to…