Related papers: Approximating the parallel transport of an induced…
We consider the problem of identifying a unitary Yang-Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with…
The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean…
High-dimensional motion planning problems can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles.…
This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for numerical optimization in Euclidean spaces. Riemannian LBFGS…
Complex Chern-Simons bundles are line bundles with connection, originating in the study of quantization of moduli spaces of flat connections with complex gauge groups. In this paper we introduce and study these bundles in the families…
Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
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…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter $H\in(1/4,1/2]$. We indicate that the phase flow preserves the symplectic…
We develop a numerical method for the martingale analogue of the Benamou--Brenier optimal transport problem, which seeks a martingale interpolating two prescribed marginals which is closest to the Brownian motion. Recent contributions have…
In this paper, we introduce a unified framework for studying various cloud traffic management problems, ranging from geographical load balancing to backbone traffic engineering. We first abstract these real-world problems as a…
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of "penalty" type for the…
Structural network embedding is a crucial step in enabling effective downstream tasks for complex systems that aims to project a network into a lower-dimensional space while preserving similarities among nodes. We introduce a simple and…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
Just as gauge theory describes the parallel transport of point particles using connections on bundles, higher gauge theory describes the parallel transport of 1-dimensional objects (e.g. strings) using 2-connections on 2-bundles. A 2-bundle…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
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…