Related papers: Diffusion of two brands in competition: cross-bran…
The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…
An agent-based model with interacting low frequency liquidity takers inter-mediated by high-frequency liquidity providers acting collectively as market makers can be used to provide realistic simulated price impact curves. This is possible…
In this paper, we study the global dynamics of a general $2\times 2$ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion…
We consider a brand with a given budget that wants to promote a product over multiple rounds of influencer marketing. In each round, it commissions an influencer to promote the product over a social network, and then observes the subsequent…
In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…
With the advent of social media, different companies often promote competing products simultaneously for word-of-mouth diffusion and adoption by users in social networks. For such scenarios of competitive diffusion, prior studies show that…
We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the…
In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where…
Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the…
We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system…
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…
We generalize the reaction-diffusion model A + B -> 0 in order to study the impact of an excess of A (or B) at the reaction front. We provide an exact solution of the model, which shows that linear response breaks down: the average…
We explore a model of duopolistic competition in which consumers learn about the fit of each competitor's product. In equilibrium, consumers comparison shop: they learn only about the relative values of the products. When information is…
Using a mean-field network formulation of the Bass innovation diffusion model and exact results by Fotouhi and Rabbat on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with…
Agents attempt to maximize expected profits earned by selling multiple units of a perishable product where their revenue streams are affected by the prices they quote as well as the distribution of other prices quoted in the market by other…
Many applications of RCTs involve the presence of multiple treatment administrators -- from field experiments to online advertising -- that compete for the subjects' attention. In the face of competition, estimating a causal effect becomes…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
As diffusion models become increasingly popular, the misuse of copyrighted and private images has emerged as a major concern. One promising solution to mitigate this issue is identifying the contribution of specific training samples in…
We discuss the equivalence between kinetic wealth-exchange models, in which agents exchange wealth during trades, and mechanical models of particles, exchanging energy during collisions. The universality of the underlying dynamics is shown…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…