相关论文: Skew 2-Dyck paths via the kernel method

Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…

We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar…

The notion of symmetric and asymmetric peaks in Dyck paths was introduced by Fl\'orez and Rodr\'{\i}guez, who counted the total number of such peaks over all Dyck paths of a given length. In this paper we generalize their results by giving…

We propose a novel, multi-layered planning approach for computing paths that satisfy both kinodynamic and spatiotemporal constraints. Our three-part framework first establishes potential sequences to meet spatial constraints, using them to…

In the recent past, automatic selection or combination of kernels (or features) based on multiple kernel learning (MKL) approaches has been receiving significant attention from various research communities. Though MKL has been extensively…

3D Scene Graphs integrate both metric and semantic information, yet their structure remains underutilized for improving path planning efficiency and interpretability. In this work, we present S-Path, a situationally-aware path planner that…

We describe a duality mapping between STRIPS planning tasks. By exchanging the initial and goal conditions, taking their respective complements, and swapping for every action its precondition and delete list, one obtains for every STRIPS…

We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic…

In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a 1-D finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinct…

This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…

We investigate the asymptotic properties of the trajectories generated by a second-order dynamical system of proximal-gradient type stated in connection with the minimization of the sum of a nonsmooth convex and a (possibly nonconvex)…

We investigate paths in the hexagonal circle packing and enumerate them with respect to width, height, number of steps, area, and kissing number. Functional equations and the kernel method yield closed bivariate generating functions…

Knowledge Graphs (KGs) are foundational to applications such as search, question answering, and recommendation. Conventional knowledge graph construction methods are predominantly static, rely ing on a single-step construction from a fixed…

The sequence A176677 in the Encyclopedia of Integer Sequences enumerates Motzkin paths where two types of horizontal steps may occur, but only on odd indexed levels. We show how to perform the enumeration, also dealing with partial such…

In the Planar Disjoint Paths problem, one is given an undirected planar graph with a set of $k$ vertex pairs $(s_i,t_i)$ and the task is to find $k$ pairwise vertex-disjoint paths such that the $i$-th path connects $s_i$ to $t_i$. We study…

The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…

We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling…

In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…

Path following controllers make the output of a control system approach and traverse a pre-specified path with no apriori time parametrization. In this paper we present a method for path following control design applicable to framed curves…

In a given 2D space, we can have points with different levels of importance. One would prefer viewing those points from a closer/farther position per their level of importance. A point in 2D from where the user can view two given points per…