Related papers: Decomposable Branching Processes and Viral Marketi…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
We study a continuous time Mutually Catalytic Branching model on the $\mathbb{Z}^{d}$. The model describes the behavior of two different populations of particles, performing random walk on the lattice in the presence of branching, that is,…
Diffusion generative models are currently the most popular generative models. However, their underlying modeling process is quite complex, and starting directly with the seminal paper Denoising Diffusion Probability Model (DDPM) can be…
The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…
Branching processes model the evolution of populations of agents that randomly generate offsprings. These processes, more patently Galton-Watson processes, are widely used to model biological, social, cognitive, and technological phenomena,…
We study the spreading dynamics on graphs with a power law degree distribution p_k ~ k^-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
A social network grows over a period of time with the formation of new connections and relations. In recent years we have witnessed a massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We introduce and study the dynamics of an \emph{immortal} critical branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is…
In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
We introduce a broad class of analytically solvable processes on networks. In the special case, they reduce to random walk and consensus process - two most basic processes on networks. Our class differs from previous models of interactions…
We investigate the long-time evolution of branching diffusion processes (starting with a single particle) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. We analyze the…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear because they are hard to predict. For theoretical models of disease spreading, on the other hand, quantities characterizing the outbreak…