相关论文: Gromov-Wasserstein Transfer Operators

We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…

We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…

Searches for gravitational waves (GWs) traditionally focus on persistent sources (e.g., pulsars or the stochastic background) or on transients sources (e.g., compact binary inspirals or core-collapse supernovae), which last for timescales…

Partial identification often arises when the joint distribution of the data is known only up to its marginals. We consider the corresponding partially identified GMM model and develop a methodology for identification, estimation, and…

Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…

Flow Matching (FM) has emerged as a powerful paradigm for continuous normalizing flows, yet standard FM implicitly performs an unweighted $L^2$ regression over the entire ambient space. In high dimensions, this leads to a fundamental…

Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…

Dynamical systems can be analyzed via their Frobenius-Perron transfer operator and its estimation from data is an active field of research. Recently entropic transfer operators have been introduced to estimate the operator of deterministic…

This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting…

Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…

Gauge invariance is a fundamental principle that must be preserved in quantum transport. However, when a complex potential is incorporated into the Hamiltonian, we find that the current described by the well-established…

We study the transport properties of passive inertial particles in a $2-d$ incompressible flows. Here the particle dynamics is represented by the $4-d$ dissipative embedding map of $2-d$ area-preserving standard map which models the…

Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen--Lo\`eve expansion. These operators may themselves be subject to variation, for…

The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…

The Sinkhorn algorithm is a widely used method for solving the optimal transport problem, and the Greenkhorn algorithm is one of its variants. While there are modified versions of these two algorithms whose computational complexities are…

Entropy-regularized optimal transport, which has strong links to the Schr\"odinger bridge problem in statistical mechanics, enjoys a variety of applications from trajectory inference to generative modeling. A major driver of renewed…

We study equivariant Gromov-Hausdorff distances for general continuous actions which are not necessarily isometric as Fukaya introduced. We prove that if an action is expansive and has pseudo-orbit tracing property then it is stable under…

The Gromov-Wasserstein (GW) distance serves as a powerful tool for matching objects in metric spaces. However, its traditional formulation is constrained to pairwise matching between single objects, limiting its utility in scenarios and…

The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel…

In this work, we derived a transport equation based on a generalized equation of time-dependent generator coordinate method (TDGCM) under the Gaussian overlap approximation (GOA). The transport equation is obtained by using…