Related papers: Probabilistic modelling and reconstruction of stra…
Eigenstrain tomography combines diffraction-based strain measurement with elasticity theory to reconstruct full three-dimensional residual stress fields within solids. Notwithstanding a number of recent examples, the uniqueness of such…
This paper introduces a method to approximate Gaussian process regression by representing the problem as a stochastic differential equation and using variational inference to approximate solutions. The approximations are compared with full…
Here we introduce a new reconstruction technique for two-dimensional Bragg Scattering Tomography (BST), based on the Radon transform models of [arXiv preprint, arXiv:2004.10961 (2020)]. Our method uses a combination of ideas from multibang…
This work considers sequential edge-promoting Bayesian experimental design for (discretized) linear inverse problems, exemplified by X-ray tomography. The process of computing a total variation type reconstruction of the absorption inside…
There has been an increasing demand for formal methods in the design process of safety-critical synthetic genetic circuits. Probabilistic model checking techniques have demonstrated significant potential in analyzing the intrinsic…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…
Ultrasound poroelastography is a cost-effective non-invasive imaging technique, which is able to reconstruct several mechanical parameters of cancer and normal tissue such as Young's modulus, Poisson's ratio, interstitial permeability and…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…
Random field and random cluster theory are used to describe certain mathematical results concerning the probability distribution of image pixel intensities characterized as generic $2D$ integer arrays. The size of the smallest bounded…
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…
We propose a novel discrete method of constructing Gaussian Random Fields (GRF) based on a combination of modified spectral representations, Fourier and Blob. The method is intended for Direct Numerical Simulations of the V-Langevin…
Nanoscale strain mapping by four-dimensional scanning transmission electron microscopy (4D-STEM) relies on determining the precise locations of Bragg-scattered electrons in a sequence of diffraction patterns, a task which is complicated by…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
The measurement of cellular traction forces on soft elastic substrates has become a standard tool for many labs working on mechanobiology. Here we review the basic principles and different variants of this approach. In general, the…
Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…