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We present a complete solution to the so-called tennis ball problem, which is equivalent to counting lattice paths in the plane that use North and East steps and lie between certain boundaries. The solution takes the form of explicit…
In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…
The dispersion process in particulate porous media at low saturation levels takes place over the surface elements of constituent particles and, as we have found previously by comparison with experiments, can be accurately described by…
In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive…
We investigate the migration of particles of different geometrical shapes and sizes in a scaled-up model of a gravity-driven deterministic lateral displacement (g-DLD) device. Specifically, particles move through a square array of…
Fibres shed from our clothes during a washing machine cycle constitute around 35% of the primary microplastics in our oceans. Current conventional dead-end washing machine filters clog relatively quickly and require frequent cleaning. We…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
Variable selection in high-dimensional spaces is a pervasive challenge in contemporary scientific exploration and decision-making. However, existing approaches that are known to enjoy strong statistical guarantees often struggle to cope…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
The Laplace approximation (LA) to posteriors is a ubiquitous tool to simplify Bayesian computation, particularly in the high-dimensional settings arising in Bayesian inverse problems. Precisely quantifying the LA accuracy is a challenging…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
In this paper, we propose two efficient, approximate formulations of the multi-sensor labelled multi-Bernoulli (LMB) filter, which both allow the sensors' measurement updates to be computed in parallel. Our first filter is based on the…
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard…
A fundamental problem in spherical distance geometry aims to recover an $n$-tuple of points on a 2-sphere in $\mathbb{R}^3$, viewed up to oriented isometry, from $O(n)$ input measurements. We solve this problem using algorithms that employ…
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…
Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…
Physics beyond the Standard Model could be measured indirectly, through its effects on Standard Model observables. One place to look for such effects is in the semileptonic decays of B mesons. In order to constrain the possible role of new…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…