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Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
This article introduces ATAB, a tool that automatically generates pairwise reachability checks for action trees. Action trees can be used to study the behaviour of real-world concurrent programs. ATAB encodes pairwise reachability checks…
Given an undirected graph and two disjoint vertex pairs $s_1,t_1$ and $s_2,t_2$, the Shortest two disjoint paths problem (S2DP) asks for the minimum total length of two vertex disjoint paths connecting $s_1$ with $t_1$, and $s_2$ with…
Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
Quadratic Programs (QPs) are widely used in the control of walking robots, especially in Model Predictive Control (MPC) and Whole-Body Control (WBC). In both cases, the controller design requires the formulation of a QP and the selection of…
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple…
Lattices are simplified by removing some of their doubly irreducible elements, resulting in smaller lattices called racks. All vertically indecomposable modular racks of $n \le 40$ elements are listed, and the numbers of all modular…
Around 2000, Ira Gessel conjectured that the number of lattice walks in the quadrant N^2, starting and ending at the origin (0,0) and taking their steps in {E,NE,W,SW} had a simple hypergeometric form. In the following decade, this problem…
We consider walks on the edges of the square lattice $\mathbb Z^2$ which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in another direction. We classify these rules according to a…
Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
The rapidly advancing fields of statistical modeling and machine learning have significantly enhanced data-driven design and optimization. This paper focuses on leveraging these design algorithms to optimize a medical walker, an integral…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
We study generative modeling of \emph{variable-length trajectories} -- sequences of visited locations/items with associated timestamps -- for downstream simulation and counterfactual analysis. A recurring practical issue is that standard…
To effectively search for the optimal motion template in dynamic multidimensional space, this paper proposes a novel optimization algorithm, Dynamic Dimension Wrapping (DDW).The algorithm combines Dynamic Time Warping (DTW) and Euclidean…
Current dynamic networks and dynamic pruning methods have shown their promising capability in reducing theoretical computation complexity. However, dynamic sparse patterns on convolutional filters fail to achieve actual acceleration in…
We study Hamiltonian walks (HWs) on the family of three--dimensional modified Sierpinski gasket fractals, as a model for compact polymers in nonhomogeneous media in three dimensions. Each member of this fractal family is labeled with an…