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Simultaneously grasping and delivering multiple objects can significantly enhance robotic work efficiency and has been a key research focus for decades. The primary challenge lies in determining how to push objects, group them, and execute…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
Recently, diffusion policy has shown impressive results in handling multi-modal tasks in robotic manipulation. However, it has fundamental limitations in out-of-distribution failures that persist due to compounding errors and its limited…
We study N interacting random walks on the positive integers. Each particle has drift {\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown…
Diffusion models have recently been successfully applied to a wide range of robotics applications for learning complex multi-modal behaviors from data. However, prior works have mostly been confined to single-robot and small-scale…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
The mathematical definitions of distinct concepts that are needed in building an ergodicity detection algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader…
We study a high throughput satellite system, where the feeder link uses free-space optical (FSO) and the user link uses radio frequency (RF) communication. In particular, we first propose a transmit diversity using Alamouti space time block…
We analyze the large time behavior of a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. It is shown, that under weak conditions this degenerate diffusion process is strong mixing,…
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-maximizing if the time average of the real-valued function f…
Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has…
In this paper we study the Heat Flow on Metric Random Walk Spaces, which unifies into a broad framework the heat flow on locally finite weighted connected graphs, the heat flow determined by finite Markov chains and some nonlocal evolution…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
In earlier papers Poisson equation in the whole space was studied for so called ergodic generators $L$ corresponding to homogeneous Markov diffusions ($X_t, \, t\ge 0$) in $\mathbb R^d$. Solving this equation is one of the main tools for…
We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics which exhibits ergodicity breaking and hysteresis in one dimension. These phenomena can be understood through a description of…
The spatial diffusion of cosmic rays in turbulent magnetic fields can, in the most general case, be fully anisotropic, i.e. one has to distinguish three diffusion axes in a local, field-aligned frame. We reexamine the transformation for the…
We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a…
Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the…