In recent years, significant progress in generative AI has highlighted the
important role of physics-inspired models that utilize advanced mathematical
concepts based on fundamental physics principles to enhance artificial
intelligence capabilities. Among these models, those based on diffusion
equations have greatly improved image quality. This study aims to explore the
potential uses of Maxwell-Boltzmann equation, which forms the basis of the
kinetic theory of gases, and the Michaelis-Menten model in Marketing Mix
Modelling (MMM) applications. We propose incorporating these equations into
Hierarchical Bayesian models to analyse consumer behaviour in the context of
advertising. These equation sets excel in accurately describing the random
dynamics in complex systems like social interactions and consumer-advertising
interactions.

本研究旨在探索 Maxwell-Boltzmann 方程和 Michaelis-Menten 模型在市场组合建模 (MMM) 应用中的潜在用途，通过将这些方程纳入分层贝叶斯模型来分析广告背景下的消费者行为，以准确描述社交互动和消费者广告互动等复杂系统中的随机动态。

基于贝叶斯方法的媒体混合建模与形状和漏斗效应

Bayesian Methods for Media Mix Modelling with shape and funnel effects

Graph neural networks (GNNs) are one of the most popular research topics for
deep learning. GNN methods typically have been designed on top of the graph
signal processing theory. In particular, diffusion equations have been widely
used for designing the core processing layer of GNNs, and therefore they are
inevitably vulnerable to the notorious oversmoothing problem. Recently, a
couple of papers paid attention to reaction equations in conjunctions with
diffusion equations. However, they all consider limited forms of reaction
equations. To this end, we present a reaction-diffusion equation-based GNN
method that considers all popular types of reaction equations in addition to
one special reaction equation designed by us. To our knowledge, our paper is
one of the most comprehensive studies on reaction-diffusion equation-based
GNNs. In our experiments with 9 datasets and 28 baselines, our method, called
GREAD, outperforms them in a majority of cases. Further synthetic data
experiments show that it mitigates the oversmoothing problem and works well for
various homophily rates.

本研究提出了一种名为 GREAD 的基于反应扩散方程的 GNN 方法，它考虑了所有流行的反应类型以及我们设计的一种特殊反应方程。在 9 个数据集和 28 个基线的实验中，我们的方法在大多数情况下都优于它们。进一步的合成数据实验表明，它缓解了过度平滑问题，并可用于各种同质化率。

GREAD：图神经反应 - 扩散网络

GREAD: Graph Neural Reaction-Diffusion Networks

We present a short overview on the strongest variational formulation for
gradient flows of geodesically $\lambda$-convex functionals in metric spaces,
with applications to diffusion equations in Wasserstein spaces of probability
measures. These notes are based on a series of lectures given by the second
author for the Summer School "Optimal transportation: Theory and applications"
in Grenoble during the week of June 22-26, 2009.

本文简要阐述了在度量空间中梯度流的最强变分形式及其在概率测度的 Wasserstein 空间中扩散方程的应用，这些笔记是第二作者在 2009 年 6 月 22 日至 26 日的格勒诺布尔夏季学校 “最优输运：理论与应用” 中所作的一系列讲座的基础。