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It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from…

Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…

We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric between a point and a half-space over the max-plus…

In stellarators, achieving effective divertor configurations is challenging due to the three-dimensional nature of the magnetic fields, which often leads to chaotic field lines and fuzzy separatrices. This work presents a novel approach to…

Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as a continuously differentiable function for any shapes other than spheres. This paper proposes a framework for…

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…

The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different…

Semantic objects are unevenly distributed over images. In this paper, we study the spatial disequilibrium problem of modern object detectors and propose to quantify this ``spatial bias'' by measuring the detection performance over zones.…

Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…

The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors of the matrices, which need to be solved numerically. We propose and analyze a…

Optimal path planning is prone to convergence to local, rather than global, optima. This is often the case for mobile manipulators due to nonconvexities induced by obstacles, robot kinematics and constraints. This paper focuses on planning…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

Multi-objective optimisation of damper placement in dynamically symmetric adjacent buildings is considered with identical viscoelastic dampers used for vibration control. First, exhaustive search is used to describe the solution space in…

This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal…

This paper presents a first contribution to the design of a small aerial robot for inhabited microgravity environments, such as orbiting space stations. In particular, we target a fleet of robots for collaborative tasks with humans, such as…

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

Positioning is becoming a key component in many Internet of Things (IoT) applications. The main challenges and limitations are the narrow bandwidth, low power and low cost which reduces the accuracy of the time of arrival (TOA) estimation.…

Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…