Related papers: Constructing stochastic flows of kernels
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…
We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we show that the laws of the flows of kernels $K$ solution of…
Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…
A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…
One main challenge for the design of networks is that traffic load is not generally known in advance. This makes it hard to adequately devote resources such as to best prevent or mitigate bottlenecks. While several authors have shown how to…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…
Spatially-periodic channels are increasingly attracting attention as an efficient alternative to packed columns for a number of analytical and engineering processes. In incompressible flows, the periodic geometry allows to compute the flow…
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel, the neural field model can be viewed as a gradient flow in…
Several aspects of the internal structure of pseudoscalar mesons, accessible through generalized parton distributions in their zero-skewness limit, are examined. These include electromagnetic and gravitational form factors related to charge…
We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N=2 supersymmetric quantum mechanics, (the proof would be the same for the Wess-Zumino model), we determine the kernels that…
We introduce a new class of nonstationary kernels, which we derive as covariance functions of a novel family of stochastic processes we refer to as string Gaussian processes (string GPs). We construct string GPs to allow for multiple types…
We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
In \cite{CMP17} a novel distributional approach has been introduced to provide a well-posed formulation of a class of crystalline mean curvature flows. In this paper, such an approach is extended to the nonlocal setting. Applications…
Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…