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A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
The wide spread use of positioning and photographing devices gives rise to a deluge of traffic trajectory data (e.g., vehicle passage records and taxi trajectory data), with each record having at least three attributes: object ID, location…
Forecast systems in science and technology are increasingly moving beyond point prediction toward methods that produce full predictive distributions of future outcomes y, conditional on high-dimensional and complex sequences of inputs x.…
Urban environments offer a challenging scenario for autonomous driving. Globally localizing information, such as a GPS signal, can be unreliable due to signal shadowing and multipath errors. Detailed a priori maps of the environment with…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
In this article we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we set out to define a proper distance measure…
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
We study the large-$N$ behavior of random matrix tuples $Y^N = (Y_1^N,\dots,Y_d^N)$ with joint density proportional to $e^{-N^2 V}$ for some convex function $V$ in non-commuting variables satisfying certain bounds on its second derivative.…
The Local-to-Global-Principle used in the proof of convexity theorems for momentum maps has been extracted as a statement of pure topology enriched with a structure of convexity. We extend this principle to not necessarily closed maps…
The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear…
We improve reliable, long-horizon, goal-directed navigation in partially-mapped environments by using non-locally available information to predict the goodness of temporally-extended actions that enter unseen space. Making predictions about…
This article provides numerical simulation of an optimal transport path from a single source to an atomic measure of equal total mass. We first construct an initial transport path, and then modify the path as much as possible by using both…
We prove that any Latt\`es map can be approximated by strictly postcritically finite rational maps which are not Latt\`es maps.
An asymptotically optimal sampling-based planner employs sampling to solve robot motion planning problems and returns paths with a cost that converges to the optimal solution cost, as the number of samples approaches infinity. This…
We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct time-dependent controls $\theta=(w, a, b)$ in the vector field…
The Kumaraswamy distribution has been proposed as an alternative to the beta distribution with more benign algebraic properties. They have the same two parameters, the same support and qualitatively similar shape for any parameter values.…
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…
Systems of a large number N of globally coupled maps have become popular as a relatively simple prototype of high-dimensional dynamics, showing many interesting and typical phenomena like synchronisation, cluster formation and…