Related papers: Aggregation-Diffusion Equations for Collective Beh…

Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Data aggregation, also known as meta analysis, is widely used to combine knowledge on parameters shared in common (e.g., average treatment effect) between multiple studies. In this paper, we introduce an attractive data aggregation scheme…

We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…

Simulation studies are commonly used to evaluate the performance of newly developed meta-analysis methods. For methodology that is developed for an aggregated data meta-analysis, researchers often resort to simulation of the aggregated data…

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of…

The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…

We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…

We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as…

Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have…

The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…

Clustering mechanisms are essential in certain multiuser networks for achieving efficient resource utilization. This lecture note presents the theory of coalition formation as a useful tool for distributed clustering problems. We reveal the…

We study numerically a coagulation-fragmentation model derived by Niwa and further elaborated by Degond et al., where a unique equilibrium distribution of group sizes is shown to exist in both cases of continuous and discrete group size…

Autoregressive (AR) models have long dominated the landscape of large language models, driving progress across a wide range of tasks. Recently, diffusion-based language models have emerged as a promising alternative, though their advantages…

In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist,…

We calculate the bulk-diffusion coefficient and the conductivity in a broad class of conserved-mass aggregation processes on a ring of discrete sites. These processes involve chipping and fragmentation of masses, which diffuse around and…

The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the…

Although numerical weather forecasting methods have dominated the field, recent advances in deep learning methods, such as diffusion models, have shown promise in ensemble weather forecasting. However, such models are typically…