相关论文: On large time behavior and selection principle for…

High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

We apply the macroscopic fluctuation theory to analyze the long-time statistics of the position of a tracer in the dense and the dilute limits of diffusive single-file systems. Our explicit results are about the corresponding large…

We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive…

In biological, glassy, and active systems, various tracers exhibit Laplace-like, i.e., exponential, spreading of the diffusing packet of particles. The limitations of the central limit theorem in fully capturing the behaviors of such…

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…

In the era of information explosion, Recommender Systems (RS) are essential for alleviating information overload and providing personalized user experiences. Recent advances in diffusion-based generative recommenders have shown promise in…

Diffusion is an ubiquitous phenomenon. It is a widespread belief that as long as the area under a current autocorrelation function converges in time, the corresponding spatiotemporal density dynamics should be diffusive. This may be viewed…

What are the key-features that enable an information diffusion model to explain the inherent dynamic, and often competitive, nature of real-world propagation phenomena? In this paper we aim to answer this question by proposing a novel class…

Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…

Sequential recommendation (SR) aims to predict items that users may be interested in based on their historical behavior sequences. We revisit SR from a novel information-theoretic perspective and find that conventional sequential modeling…

Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains…

Wavelength selection in reaction--diffusion systems can be understood as a coarsening process that is interrupted by counteracting processes at certain wavelengths. We first show that coarsening in mass-conserving systems is driven by…

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

The problem of model selection is inevitable in an increasingly large number of applications involving partial theoretical knowledge and vast amounts of information, like in medicine, biology or economics. The associated techniques are…

Motivated by recent experiments we consider a stochastic lineshape theory for the case when the underlying process obeys power-law statistics, based on a generalized Anderson-Kubo oscillator model. We derive an analytical expression for the…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…

The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…