Related papers: A Novel Exploration of Diffusion Process based on …
The Arnold diffusion constitutes a dynamical phenomenon which may occur in the phase space of a non-integrable Hamiltonian system whenever the number of the system degrees of freedom is $M \geq 3$. The diffusion is mediated by a web-like…
Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this…
Recently, diffusion-based recommendation methods have achieved impressive results. However, existing approaches predominantly treat each user's historical interactions as independent training samples, overlooking the potential of…
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…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Text-to-3D, known for its efficient generation methods and expansive creative potential, has garnered significant attention in the AIGC domain. However, the pixel-wise rendering of NeRF and its ray marching light sampling constrain the…
Creating accurate and geologically realistic reservoir facies based on limited measurements is crucial for field development and reservoir management, especially in the oil and gas sector. Traditional two-point geostatistics, while…
We study a classical multitype Galton--Watson process with mutation and selection. The individuals are sequences of fixed length over a finite alphabet. On the sharp peak fitness landscape together with independent mutations per locus, we…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook…
Network cascade refers to diffusion processes in which outcome changes within part of an interconnected population trigger a sequence of changes across the entire network. These cascades are governed by underlying diffusion networks, which…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
Diffusion models have demonstrated highly-expressive generative capabilities in vision and NLP. Recent studies in reinforcement learning (RL) have shown that diffusion models are also powerful in modeling complex policies or trajectories in…
Cellular responses often require the fast activation or repression of specific genes, which depends on Transcription Factors (TFs) that have to quickly find the promoters of these genes within a large genome. Transcription Factors (TFs)…
Most networks tend to show complex and multiple relationships between entities. Networks are usually modeled by graphs or hypergraphs; nonetheless a given entity can occur many times in a relationship: this brings the need to deal with…
Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…
Social contagion has been studied in various contexts. Many instances of social contagion can be modeled as an infection process where a specific state (adoption of product, fad, knowledge, behavior, etc.) spreads from individual to…
Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton-Watson trees. For example, let $\mathcal{T}_1$ be the…
Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…
We employ the framework of multitype Galton-Watson processes to model a population of dividing cells. The cellular type is represented by its biological age, defined as the count of harmful proteins hosted by the cell. The stochastic…