Related papers: Matrix Analysis of Tracer Transport
The constrained orthogonal Procrustes problem is the least-squares problem that calls for a rotation matrix that optimally aligns two corresponding sets of points in d-dimensional Euclidean space. This problem generalizes to the so-called…
The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose,…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
We propose an algorithm for solution of high-dimensional evolutionary equations (ODEs and discretized time-dependent PDEs) in the Tensor Train (TT) decomposition, assuming that the solution and the right-hand side of the ODE admit such a…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The considered scenario consists of several ground terminals (GTs) communicating with the UAVs using variable transmission power and fixed data rate.…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
By means of Ito calculus it is possible to find, in a straight-forward way, the analytical solution to some equations related to the passive tracer transport problem in a velocity field that obeys the multidimensional Burgers equation and…
In this paper, we present a new method for the solution of those linear transport processes that may be described by a Master Equation, such as electron, neutron and photon transport, and more exotic variants thereof. We base our algorithm…
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All…
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…
High-dimensional partial differential equations (PDEs) are ubiquitous in economics, science and engineering. However, their numerical treatment poses formidable challenges since traditional grid-based methods tend to be frustrated by the…
This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complex-steerable pyramid.…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolation-like porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the…
An algorithm for solving the random resistor problem by means of the transfer-matrix approach is presented. Preconditioning by spanning clusters extraction both reduces the size of the conductivity matrix and speed up the calculations.
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…