Related papers: Boundary Effects in the Discrete Bass Model

Does a new product spread faster among heterogeneous or homogeneous consumers? We analyze this question using the stochastic discrete Bass model, in which consumers may differ in their individual external influence rates $\{p_j \}$ and in…

We consider the diffusion of new products in the discrete Bass-SIR model, in which consumers who adopt the product can later "recover" and stop influencing their peers to adopt the product. To gain insight into the effect of the social…

We analyze the effect of boundaries in the discrete Bass model on D-dimensional Cartesian networks. In 2D, this model describes the diffusion of new products that spread primarily by spatial peer effects, such as residential photovoltaic…

We derive novel analytic tools for the discrete Bass model, which models the diffusion of new products on networks. We prove that the probability that any two nodes adopt by time t, is greater than or equal to the product of the…

This paper introduces a measure of the diffusion of binary outcomes over a large, sparse network, when the diffusion is observed in two time periods. The measure captures the aggregated spillover effect of the state-switches in the initial…

We study the equilibrium points of a system of equations corresponding to a Bass based model that describes the diffusion of two brands in competition. To increase the understanding of the effects of the cross-brand parameters, we perform a…

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…

Spreading (diffusion) of innovations is a stochastic process on social networks. When the key driving mechanism is peer effects (word of mouth), the rate at which the aggregate adoption level increases with time depends strongly on the…

We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…

The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate…

Dynamic models and statistical inference for the diffusion of information in social networks is an area which has witnessed remarkable progress in the last decade due to the proliferation of social networks. Modeling and inference of…

In the moderately long wavelength propagation regime, acoustic crystaldevices which size is of several wave lengths are studied by using thefinite-difference time domain method. It is shown by the focusing and imaging of a square shaped…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to…

We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but…

Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…

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…

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 present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…

Knowledge acquisition by consumers is a key process in the diffusion of innovations. However, in standard theories of the representative agent, agents do not learn and innovations are adopted instantaneously. Here, we show that in a…