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This paper considers stochastic monotone variational inequalities whose feasible region is the intersection of a (possibly infinite) number of convex functional level sets. A projection-based approach or direct Lagrangian-based techniques…

The last improvements in programming languages, programming models, and frameworks have focused on abstracting the users from many programming issues. Among others, recent programming frameworks include simpler syntax, automatic memory…

We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…

This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…

We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete…

In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…

We study a cellular automaton (CA) model of information dynamics on a single hypha of a fungal mycelium. Such a filament is divided in compartments (here also called cells) by septa. These septa are invaginations of the cell wall and their…

Generative models such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) have shown promise in sequential recommendation tasks. However, they face challenges, including posterior collapse and limited…

The two dimensional directed sandpile with dissipation is transformed into a (1+1) dimensional problem with discrete space and continuous `time'. The master equation for the conditional probability that K grains preserve their initial order…

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a…

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…

Given an initial distribution of sand in an Abelian sandpile, what final state does it relax to after all possible avalanches have taken place? In d >= 3, we show that this problem is P-complete, so that explicit simulation of the system is…

Let $\alpha=1/2$, $\theta>-1/2$, and $\nu_0$ be a probability measure on a type space $S$. In this paper, we investigate the stochastic dynamic model for the two-parameter Dirichlet process $\Pi_{\alpha,\theta,\nu_0}$. If $S=\mathbb{N}$, we…

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

Offline decision-making via diffusion models often produces trajectories that are misaligned with system dynamics, limiting their reliability for control. We propose Model Predictive Diffuser (MPDiffuser), a compositional diffusion…

Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…

The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…

We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian…

Generating high-resolution images with generative models has recently been made widely accessible by leveraging diffusion models pre-trained on large-scale datasets. Various techniques, such as MultiDiffusion and SyncDiffusion, have further…