相关论文: Causal transport on path space

Determining causal relationship between high dimensional observations are among the most important tasks in scientific discoveries. In this paper, we revisited the \emph{linear trace method}, a technique proposed…

Spatial coupling has recently emerged as a powerful paradigm to construct graphical models that work well under low-complexity message-passing algorithms. Although much progress has been made on the analysis of spatially coupled models…

We give a sufficient and necessary condition for a probability measure $\mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and…

We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero…

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…

We develop a novel theory of weak and strong stochastic integration for cylindrical martingale-valued measures taking values in the dual of a nuclear space. This is applied to develop a theory of SPDEs with rather general coefficients. In…

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…

We investigate energy transport in several two-level atom or spin-1/2 models by a direct coupling to heat baths of different temperatures. The analysis is carried out on the basis of a recently derived quantum master equation which…

Causal inference in cue combination is to decide whether the cues have a single cause or multiple causes. Although the Bayesian causal inference model explains the problem of causal inference in cue combination successfully, how causal…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

Magnetic resonance methods offer a unique chance for in-depth study of conductive organic material systems, not only accounts for number of charge carriers, but also allows manipulations of spin dynamics of particles. Here we present a…

This is an expository paper describing how duality theory for Hessian manifolds provides a natural setting for optimal transport. We explain how this can be used to solve Monge-Amp\`ere equations and survey recent results along these lines…

Positional encoding is essential for supplementing transformer with positional information of tokens. Existing positional encoding methods demand predefined token/feature order, rendering them unsuitable for real-world data with…

We study the isentropic compressible Euler equations in multi-dimensions with stochastic perturbation of transport type. On the one hand, this is motivated by the physical modelling in turbulence theory. On the other hand, it has been shown…

Transport properties of one-dimensional Kronig-Penney models with binary correlated disorder are analyzed using an approach based on classical Hamiltonian maps. In this method, extended states correspond to bound trajectories in the phase…

By using Lyapunov conditions, weak Poincar\'e inequalities are established for some probability measures on a manifold $(M,g)$. These results are further applied to the convolution of two probability measures on $\R^d$. Along with explicit…

Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a new type of Monge-Ampere measure on X, defined for singular…

Inside cells, various cargos are transported by teams of molecular motors. Intriguingly, the motors involved generally have opposite pulling directions, and the resulting cargo dynamics is a biased stochastic motion. It is an open question…

We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called {\em causal relation}, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of…

A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective…