Related papers: Exact sampling of self-avoiding paths via discrete…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
We show a connection between sampling and optimization on discrete domains. For a family of distributions $\mu$ defined on size $k$ subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of…
For many tasks, predictive path-following control can significantly improve the performance and robustness of autonomous robots over traditional trajectory tracking control. It does this by prioritizing closeness to the path over timed…
For aerial swarms, navigation in a prescribed formation is widely practiced in various scenarios. However, the associated planning strategies typically lack the capability of avoiding obstacles in cluttered environments. To address this…
Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…
Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one of the most difficult problems of enumerative combinatorics. Once we give up calculating the exact number of them, however, we have a chance to apply powerful…
This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…
The self-avoiding walk, and lattice spin systems such as the $\varphi^4$ model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical…
This paper proposes a 2-D autonomous exploration and mapping framework for LiDAR-based SLAM mobile robots, designed to address the major challenges on low-cost platforms, including process instability, map drift, and increased risks of…
An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology…
We study downward deviations of the boundary of the range of a transient walk on the Euclidean lattice. We describe the optimal strategy adopted by the walk in order to shrink the boundary of its range. The technics we develop apply equally…
We present a real space renormalization-group map for probabilities of random walks on a hierarchical lattice. From this, we study the asymptotic behavior of the end-to-end distance of a weakly self- avoiding random walk (SARW) that…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
In the last few years, new insights have permitted unexpected progress in the study of fractal shapes in two dimensions. A new approach, called Schramm-Loewner evolution, or SLE, has arisen through analytic function theory and probability…
In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization…
This paper is concerned with the adaptive numerical treatment of stochastic partial differential equations. Our method of choice is Rothe's method. We use the implicit Euler scheme for the time discretization. Consequently, in each step, an…
We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of…
We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…