Related papers: Automatic Counting of Restricted Dyck Paths via (N…
An $(a,b)$-Dyck path $P$ is a lattice path from $(0,0)$ to $(b,a)$ that stays above the line $y=\frac{a}{b}x$. The zeta map is a curious rule that maps the set of $(a,b)$-Dyck paths into itself; it is conjecturally bijective, and we provide…
Most of the existing knowledge graphs are not usually complete and can be complemented by some reasoning algorithms. The reasoning method based on path features is widely used in the field of knowledge graph reasoning and completion on…
This paper explores a novel dynamic network for vision and language tasks, where the inferring structure is customized on the fly for different inputs. Most previous state-of-the-art approaches are static and hand-crafted networks, which…
In this paper, we investigate combining blocking and collapsing -- two widely used strategies for improving the accuracy of Gibbs sampling -- in the context of probabilistic graphical models (PGMs). We show that combining them is not…
In the spirit of "multi-culturalism", we use four kinds of computations: simulation, numeric, symbolic, and "conceptual" to explore some "games of pure chance" inspired by children board games like "Snakes and Ladders" (aka as "Chutes and…
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…
We present a method of automatically synthesizing steps to solve search problems. Given a specification of a search problem, our approach uses symbolic execution to analyze the specification in order to extract a set of constraints which…
We consider the set of alternating paths on a fixed fully packed loop of size n. This set is in bijection with the set of fully packed loops of size n. Furthermore, for a special choice of fully packed loop, we demonstrate that the set of…
Many real-world sequential manipulation tasks involve a combination of discrete symbolic search and continuous motion planning, collectively known as combined task and motion planning (TAMP). However, prevailing methods often struggle with…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Near-term large quantum computers are not able to operate as a single processing unit. It is therefore required to partition a quantum circuit into smaller parts, and then each part is executed on a small unit. This approach is known as…
Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
Constraint programming is used for a variety of real-world optimisation problems, such as planning, scheduling and resource allocation problems. At the same time, one continuously gathers vast amounts of data about these problems. Current…
Among sub-optimal Multi-Agent Path Finding (MAPF) solvers, rule-based algorithms are particularly appealing since they are complete. Even in crowded scenarios, they allow finding a feasible solution that brings each agent to its target,…
We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…