相关论文: Flows, coalescence and noise

Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…

From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…

A two-dimensional array of independent random signs produces coalescing random walks. The position of the walk, starting at the origin, after N steps is a highly nonlinear, noise sensitive function of the signs. A typical term of its…

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would…

This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…

The formulation of a model for the evolution of the flow of a solid-liquid mixture (coal-water) in a horizontal pipeline with partial phase separation is the aim of this work. Problems of instabilities due to complex eigenvalues, observed…

Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a…

We consider an SDE in R^m of the type dX(t)=a(X(t))dt+dU(t) with a L\'evy process U and study the problem for the distribution of a solution to be regular in various senses. We do not impose any specific conditions on the L\'evy measure of…

In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a…

Reinforcement learning (RL) has become an effective way to improve prompt alignment and perceptual quality in diffusion and flow-matching generators. A critical step for applying online RL to flow matching is turning the deterministic…

We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…

Normalizing flows are a class of generative models that enable exact likelihood evaluation. While these models have already found various applications in particle physics, normalizing flows are not flexible enough to model many of the…

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model…

We prove universality of a macroscopic behavior of solutions of a large class of semi-linear parabolic SPDEs on $\mathbb{R}_+\times\mathbb{T}$ with fractional Laplacian $(-\Delta)^{\sigma/2}$, additive noise and polynomial non-linearity,…

This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are…

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…