Related papers: The Bass diffusion model: agent-based implementati…
We consider an agent-based model in which two types of agents interact locally over a graph and have a common intolerance threshold $\tau$ for changing their types with exponentially distributed waiting times. The model is equivalent to an…
Despite the impressive capabilities of large language models, their substantial computational costs, latency, and privacy risks hinder their widespread deployment in real-world applications. Small Language Models (SLMs) with fewer than 10…
Over the years, population-level tobacco control policies have considerably reduced smoking prevalence worldwide. However, the rate of decline of smoking prevalence is slowing down. Therefore, there is a need for models that capture the…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
Text-to-image diffusion models can synthesize high-quality images, yet the outcome is notoriously sensitive to the random seed: different initial seeds often yield large variations in image quality and prompt-image alignment. We revisit…
We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barab\'{a}si and Albert where a network is generated iteratively from a small seed…
How does social network structure amplify or stifle behavior diffusion? Existing theory suggests that when social reinforcement makes the adoption of behavior more likely, it should spread more -- both farther and faster -- on clustered…
Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive…
The introduction of new generation hyperspectral satellite sensors, combined with advancements in deep learning methodologies, has significantly enhanced the ability to discriminate detailed land-cover classes at medium-large scales.…
This paper models information diffusion in a network of Large Language Models (LLMs) that is designed to answer queries from distributed datasets, where the LLMs can hallucinate the answer. We introduce a two-time-scale dynamical model for…
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…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
Social science research increasingly benefits from statistical methods for understanding the structured nature of social life, including for social network data. However, the application of statistical network models within large-scale…
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…
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 present a modified diffusive epidemic process that has a finite threshold on scale-free graphs. The diffusive epidemic process describes the epidemic spreading in a non-sedentary population, and it is a reaction-diffusion process. In the…
Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…