Related papers: Relativistic minimization with constraints: A smoo…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
The problem is discussed of whether a traveller can reach a remote object and return back sooner than a photon would when taken into account that the traveller can partly control the geometry of his world. It is argued that under some…
We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…
We study generic solutions in a non-minimally coupled to gravity scalar field cosmology. It is shown that dynamics for both canonical and phantoms scalar fields with the potential can be reduced to the dynamical system from which the exact…
Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics.…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
We model accelerated trips at high-velocity aboard light sails (beam-powered propulsion in general) and radiation rockets (thrust by anisotropic emission of radiation) in terms of Kinnersley's solution of general relativity and its…
General relativistic entropic acceleration theory may explain the present cosmic acceleration from first principles without the need of introducing a cosmological constant. Following the covariant formulation of non-equilibrium phenomena in…
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…
Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a…
Wallace (2022) has recently argued that a number of popular approaches to the measurement problem can't be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only…
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…
The standard LP relaxation of the asymmetric traveling salesman problem has been conjectured to have a constant integrality gap in the metric case. We prove this conjecture when restricted to shortest path metrics of node-weighted digraphs.…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an…
Consider a frictionless surface S in a gravitational field that need not be uniform. Given two points A and B on S, what curve is traced out by a particle that starts at A and reaches B in the shortest time? This paper considers this…
We study the effects of relativistic motion on quantum teleportation and propose a realizable experiment where our results can be tested. We compute bounds on the optimal fidelity of teleportation when one of the observers undergoes…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
We design optimal harmonic-trap trajectories to transport cold atoms without final excitation, combining an inverse engineering techniqe based on Lewis-Riesenfeld invariants with optimal control theory. Since actual traps are not really…