Related papers: Boundary Effects in the Discrete Bass Model
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
As a widely observable social effect, influence diffusion refers to a process where innovations, trends, awareness, etc. spread across the network via the social impact among individuals. Motivated by such social effect, the concept of…
In this work, the aim is to study the diffusion of innovation of two competing products. The main focus has been to understand the effects of the competitive dynamic market on the diffusion of innovation. The global smartphone operating…
Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…
The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one,…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional…
Recently, online social networks have become major battlegrounds for political campaigns, viral marketing, and the dissemination of news. As a consequence, ''bad actors'' are increasingly exploiting these platforms, becoming a key challenge…
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…
We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche. This model consists of a system of coupled…
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks…
The primary axes of interest in image-generating diffusion models are image quality, the amount of variation in the results, and how well the results align with a given condition, e.g., a class label or a text prompt. The popular…
Influence overlap is a universal phenomenon in influence spreading for social networks. In this paper, we argue that the redundant influence generated by influence overlap cause negative effect for maximizing spreading influence. Firstly,…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
A pivotal idea in network science, marketing research and innovation diffusion theories is that a small group of nodes -- called influencers -- have the largest impact on social contagion and epidemic processes in networks. Despite the…