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When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…

The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve…

A new method for the solution of initial-boundary value problems for evolution PDEs recently introduced by Fokas is generalised to multidimensions. Also the relation of this method with the method of images and with the classical integral…

Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely…

We study a generalization of Swendsen-Wang algorithm suited for Potts models with next-next-neighborhood interactions. Using the embedding technique proposed by Wolff we test it on the Symanzik improved bidimensional non-linear $\sigma$…

We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…

In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate…

As the prediction horizon increases, predicting the future evolution of traffic scenes becomes increasingly difficult due to the multi-modal nature of agent motion. Most state-of-the-art (SotA) prediction models primarily focus on…

Recent advances in diffusion models have set an impressive milestone in many generation tasks, and trending works such as DALL-E2, Imagen, and Stable Diffusion have attracted great interest. Despite the rapid landscape changes, recent new…

In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Spontaneous stratification of granular mixtures has been reported by Makse et al. [Nature 386, 379 (1997)] when a mixture of grains differing in size and shape is poured in a quasi-two-dimensional heap. We study this phenomenon using two…

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…

When tracking a large number of targets, it is often computationally expensive to represent the full joint distribution over target states. In cases where the targets move independently, each target can instead be tracked with a separate…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

The pebble-motion on graphs is a subcategory of multi-agent pathfinding problems dealing with moving multiple pebble-like objects from a node to a node in a graph with a constraint that only one pebble can occupy one node at a given time.…

The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal…

Suppose X is a multivariate diffusion process that is observed discretely in time. At each observation time, a transformation of the state of the process is observed with noise. The smoothing problem consists of recovering the path of the…

Beam alignment is a key challenge in directional mmWave and THz systems, where narrow beams require accurate yet low-overhead training. Existing learning-based approaches typically predict a single beam and do not quantify uncertainty,…