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1. Boundary Sketching with Asymptotically Optimal Distance and Rotation

   Dani, Varsha; Islam, Abir; Saia, Jared (July 2023, Structural Information and Communication Complexity)

   Rajsbaum, Sergio; Balliu, Alkida; Daymude, Joshua J.; Olivetti, Dennis (Ed.)

   We address the problem of designing a distributed algorithm for two robots that sketches the boundary of an unknown shape. Critically, we assume a certain amount of delay in how quickly our robots can react to external feedback. In particular, when a robot moves, it commits to move along path of length at least λ, or turn an amount of radians at least λ for some positive λ ≤ (1/2)^6, that is normalized based on a unit diameter shape. Then, our algorithm outputs a polygon that is an ϵ-sketch, for ϵ = 8λ^(1/2), in the sense that every point on the shape boundary is within distance ϵ of the output polygon. Moreover, our costs are asymptotically optimal in two key criteria for the robots: total distance travelled and total amount of rotation. Additionally, we implement our algorithm, and illustrate its output on some specific shapes. 

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2. Machine-assisted discovery of integrable symplectic mappings

   https://doi.org/10.1103/PhysRevResearch.5.043241  

   Zolkin, T.; Kharkov, Y.; Nagaitsev, S. (December 2023, Physical Review Research)

   We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e., integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and ultradiscrete Painlevé equations. In total, over 100 new integrable families are presented and analyzed; some of them are isolated in the space of parameters, and some of them are families with one parameter (or the ratio of parameters) being continuous or discrete. At the end of the paper, we suggest how newly discovered maps are related to a general 2D symplectic map via an introduction of discrete perturbation theory and propose a method on how to construct smooth near-integrable dynamical systems based on mappings with polygon invariants. 

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3. Forming and Controlling Hitches in Midair Using Aerial Robots

   https://doi.org/10.1109/ICRA48891.2023.10160741  

   D’Antonio, Diego S; Bhattacharya, Subhrajit; Saldaña, David (May 2023, Proceedings of the IEEE International Conference on Robotics and Automation (ICRA))

   The use of cables for aerial manipulation has shown to be a lightweight and versatile way to interact with objects. However, fastening objects using cables is still a challenge and human is required. In this work, we propose a novel way to secure objects using hitches. The hitch can be formed and morphed in midair using a team of aerial robots with cables. The hitch's shape is modeled as a convex polygon, making it versatile and adaptable to a wide variety of objects. We propose an algorithm to form the hitch systematically. The steps can run in parallel, allowing hitches with a large number of robots to be formed in constant time. We develop a set of actions that include different actions to change the shape of the hitch. We demonstrate our methods using a team of aerial robots via simulation and actual experiments. 

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4. A pre-expectation calculus for probabilistic sensitivity

   https://doi.org/10.1145/3434333  

   Aguirre, Alejandro; Barthe, Gilles; Hsu, Justin; Kaminski, Benjamin Lucien; Katoen, Joost-Pieter; Matheja, Christoph (January 2021, Proceedings of the ACM on Programming Languages)

   null (Ed.)

   Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow. 

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5. Efficient Parallel Output-Sensitive Edit Distance

   https://doi.org/10.4230/LIPIcs.ESA.2023.40  

   Ding, Xiangyun; Dong, Xiaojun; Gu, Yan; Liu, Youzhe; Sun, Yihan (September 2023, 31st Annual European Symposium on Algorithms (ESA 2023))

   Gørtz, Inge Li; Farach-Colton, Martin; Puglisi, Simon J.; Herman, Grzegorz (Ed.)

   In this paper, we study efficient parallel edit distance algorithms, both in theory and in practice. Given two strings A[1..n] and B[1..m], and a set of operations allowed to edit the strings, the edit distance between A and B is the minimum number of operations required to transform A into B. In this paper, we use edit distance to refer to the Levenshtein distance, which allows for unit-cost single-character edits (insertions, deletions, substitutions). Sequentially, a standard Dynamic Programming (DP) algorithm solves edit distance with Θ(nm) cost. In many real-world applications, the strings to be compared are similar to each other and have small edit distances. To achieve highly practical implementations, we focus on output-sensitive parallel edit-distance algorithms, i.e., to achieve asymptotically better cost bounds than the standard Θ(nm) algorithm when the edit distance is small. We study four algorithms in the paper, including three algorithms based on Breadth-First Search (BFS), and one algorithm based on Divide-and-Conquer (DaC). Our BFS-based solution is based on the Landau-Vishkin algorithm. We implement three different data structures for the longest common prefix (LCP) queries needed in the algorithm: the classic solution using parallel suffix array, and two hash-based solutions proposed in this paper. Our DaC-based solution is inspired by the output-insensitive solution proposed by Apostolico et al., and we propose a non-trivial adaption to make it output-sensitive. All of the algorithms studied in this paper have good theoretical guarantees, and they achieve different tradeoffs between work (total number of operations), span (longest dependence chain in the computation), and space. We test and compare our algorithms on both synthetic data and real-world data, including DNA sequences, Wikipedia texts, GitHub repositories, etc. Our BFS-based algorithms outperform the existing parallel edit-distance implementation in ParlayLib in all test cases. On cases with fewer than 10⁵ edits, our algorithm can process input sequences of size 10⁹ in about ten seconds, while ParlayLib can only process sequences of sizes up to 10⁶ in the same amount of time. By comparing our algorithms, we also provide a better understanding of the choice of algorithms for different input patterns. We believe that our paper is the first systematic study in the theory and practice of parallel edit distance. 

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