Related papers: Exact sampling of self-avoiding paths via discrete…
Autonomous 3D acquisition of outdoor environments poses special challenges. Different from indoor scenes, where the room space is delineated by clear boundaries and separations (e.g., walls and furniture), an outdoor environment is spacious…
We study downward deviations of the maximum local time of the discrete-time simple random walk on $\mathbb{Z}^d$, $d\ge 3$. In our previous paper \cite{li2026ldmaxlocal}, the corresponding upper bound was established, while the matching…
We enumerate self-avoiding walks and polygons, counted by perimeter, on the quasiperiodic rhombic Penrose and Ammann-Beenker tilings, thereby considerably extending previous results. In contrast to similar problems on regular lattices,…
Solutions to linear controlled differential equations can be expressed in terms of iterated path integrals of the driving path. This collection of iterated integrals encodes essentially all information about the driving path. While upper…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
Navigating an arbitrary-shaped ground robot safely in cluttered environments remains a challenging problem. The existing trajectory planners that account for the robot's physical geometry severely suffer from the intractable runtime. To…
Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was…
We derive some large deviation bounds for events related to the "true self-repelling motion", a one-dimensional self-interacting process introduced by Toth and Werner, that has very different path properties than usual diffusion processes.…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We have developed a parallel algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 110. We have also extended the series for the first 10 area-weighted moments and the radius of…
In this paper, we consider the minimization of a $C^2-$smooth and strongly convex objective depending on a given parameter, which is usually found in many practical applications. We suppose that we desire to solve the problem with some…
This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that…
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the…
This is an exposition of the theorem from the title, which says that the number of self-avoiding walks with n steps in the hexagonal lattice has asymptotics (2cos(pi/8))^{n+o(n)}. We lift the key identity to formal level and simplify the…
Autonomous driving vehicles aim to free the hands of vehicle operators, helping them to drive easier and faster, meanwhile, improving the safety of driving on the highway or in complex scenarios. Automated driving systems (ADS) are…
Appreciation of Stochastic Loewner evolution (SLE$_\kappa$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal…
In the present work, we revisit the topic of translational eigenmodes in discrete models. We focus on the prototypical example of the discrete nonlinear Schr{\"o}dinger equation, although the methodology presented is quite general. We…
We consider a variation of Dyck paths, where additionally to steps $(1,1)$ and $(1,-1)$ down-steps $(1,-j)$, for $j\ge2$ are allowed. We give credits to Emeric Deutsch for that. The enumeration of such objects living in a strip is…