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We consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are…
Pair-collision between viscous drops in a confined shear is numerically simulated to show that the confinement drastically alters the trajectories of the drops. In contrast to free shear, drops here move towards the centerline giving rise…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
A triangulation of a point configuration is regular if it can be given by a height function, that is every point gets lifted to a certain height and projecting the lower convex hull gives the triangulation. Checking regularity of a…
In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for…
Finding an unsupervised decomposition of an image into individual objects is a key step to leverage compositionality and to perform symbolic reasoning. Traditionally, this problem is solved using amortized inference, which does not…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…
A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and…
To simulate open boundaries within finite computation domain, real-function coordinate transformation in the framework of generally covariant formulation of Maxwell equations is proposed. The mapping--realized with arctangent function…
We propose a spatial discretization of the fourth-order nonlinear DLSS equation on the circle. Our choice of discretization is motivated by a novel gradient flow formulation with respect to a metric that generalizes martingale transport.…
In this paper we consider the resolvent Stokes problem in the case there is a small perturbation of the domain caused by a perturbed boundary. Firstly, we prove that the solution of Stokes problem is continuous due to this small…
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the…
The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…
We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…