Related papers: Optimal separator for an hyperbola; Application to…
This paper considers target tracking based on a beacon signal's time-difference-of-arrival (TDOA) to a group of cooperating sensors. The sensors receive a reflected signal from the target where the time-of-arrival (TOA) renders the distance…
We present a position operator that is compatible with periodic boundary conditions (PBC). It is a one-body operator that can be applied in calculations of correlated materials by simply replacing the traditional position vector by the new…
We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard…
In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal…
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…
Motivated by an intention to apply partial wave analysis to systems containing photons, we construct eigenvectors of the distance of separation between two photons. A choice is made that makes the case of two photons most closely resemble…
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
Object rearrangement in a multi-room setup should produce a reasonable plan that reduces the agent's overall travel and the number of steps. Recent state-of-the-art methods fail to produce such plans because they rely on explicit…
Obstacle avoidance is one of the essential and indispensable functions for autonomous mobile robots. Most of the existing solutions are typically based on single condition constraint and cannot incorporate sensor data in a real-time manner,…
When using constellation synergy to image large areas for reconnaissance, it is required to achieve the coverage capability requirements with minimal consumption of observation resources to obtain the most optimal constellation observation…
In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a…
We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms…
We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
The signal registered by a plane photodetector placed behind an optically inhomogeneous object irradiated by two coherent Gaussian beams intersecting inside the object at small angle to each other is calculated in the single-scattering…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
In this paper, we present a novel strategy to compute minimum-time trajectories for quadrotors in constrained environments. In particular, we consider the motion in a given flying region with obstacles and take into account the physical…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…