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An automated and reliable processing of bubbly flow images is highly needed to analyse large data sets of comprehensive experimental series. A particular difficulty arises due to overlapping bubble projections in recorded images, which…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
The problem of determining the manner in which an incoming acoustic wave is scattered by an elastic body immersed in a fluid is one of central importance in detecting and identifying submerged objects. The problem is generally referred to…
Long DNA molecules can be mapped by cutting them with restriction enzymes inside a narrow channel. Once cut, the individual fragments thus produced move away from each other due to diffusion and entropic effects. We investigate how long it…
Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the law of the perturbations, we construct a translation-invariant…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis-parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the…
Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of…
Entangled matter provides intriguing perspectives in terms of deformation mechanisms, mechanical properties, assembly and disassembly. However, collective entanglement mechanisms are complex, occur over multiple length scales, and they are…
In this work is provided a numerical study of a diffusion problem involving a second order term on the domain boundary (the Laplace-Beltrami operator) referred to as the \textit{Ventcel problem}.A variational formulation of the Ventcel…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
Nonlinear filtering with standard PF methods requires mitigative techniques to quell weight degeneracy, such as resampling. This is especially true in high-dimensional systems with sparse observations. Unfortunately, such techniques are…
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…