Related papers: High-Dimensional Diffusive Growth
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment.…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
During the last decade, self-affine geometrical properties of many growing aggregates, originated in a wide variety of processes, have been well characterized. However, little progress has been achieved in the search of a unified…
The success of agricultural artificial intelligence depends heavily on large, diverse, and high-quality plant image datasets, yet collecting such data in real field conditions is costly, labor intensive, and seasonally constrained. This…
We study a stochastic model of urban growth generating spatial distributions of population densities at an intermediate mesoscopic scale. The model is based on the antagonist interplay between the two opposite abstract processes of…
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
While the community of 3D point cloud generation has witnessed a big growth in recent years, there still lacks an effective way to enable intuitive user control in the generation process, hence limiting the general utility of such methods.…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion…
Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be…
When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may…
We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form…
We consider diffusion limited aggregation of particles of two different kinds. It is assumed that a particle of one kind may adhere only to another particle of the same kind. The particles aggregate on a linear substrate which consists of…
Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the…
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the…
The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo…
We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to $10^8$ particles). We observe that DLA clusters undergo strongly anisotropic…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…