Related papers: Finding matched rms envelopes in rf linacs: A Hami…
This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary $\mathcal{D}$ in a Hilbert space $\mathcal{H}$. Given an element $f\in \mathcal{H}$, OMP generates a sequence of…
Transportation researchers and planners utilize a wide range of roadway metrics that are usually associated with different basemaps. Conflation is an important process for transferring these metrics onto a single basemap. However,…
The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…
The hamiltonian circuit polytope is the convex hull of feasible solutions for the circuit constraint, which provides a succinct formulation of the traveling salesman and other sequencing problems. We study the polytope by establishing its…
The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…
We study algorithms for matching user tracks, consisting of time-ordered location points, to paths in the road network. Previous work has focused on the scenario where the location data is linearly ordered and consists of fairly dense and…
Seismic travel time tomography is a geophysical imaging method to infer the 3-D interior structure of the solid Earth. Most commonly formulated as a linear(ized) inverse problem, it maps differences between observed and expected wave travel…
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…
To efficiently deploy robotic systems in society, mobile robots must move autonomously and safely through complex environments. Nonlinear model predictive control (MPC) methods provide a natural way to find a dynamically feasible trajectory…
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In…
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recovers the original system but also yields different real…
Riemannian optimization uses local methods to solve optimization problems whose constraint set is a smooth manifold. A linear step along some descent direction usually leaves the constraints, and hence retraction maps are used to…
Most existing matching algorithms are one-off algorithms, i.e., they usually measure the distance between the two image feature representation vectors for only one time. In contrast, human's vision system achieves this task, i.e., image…
Hamiltonian Monte Carlo (HMC) improves the computational efficiency of the Metropolis algorithm by reducing its random walk behavior. Riemannian Manifold HMC (RMHMC) further improves HMC's performance by exploiting the geometric properties…
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are…
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…
To analyze nonlinear dynamic systems, we developed a new technique based on the square matrix method. We propose this technique called the \convergence map" for generating particle stability diagrams similar to the frequency maps widely…
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…