Related papers: A dynamical algorithm to compute hyperbolic Julia …
Many high-dimensional practical data sets have hierarchical structures induced by graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional embeddings in other space forms to perform…
We are given a set of $n$ jobs and a single processor that can vary its speed dynamically. Each job $J_j$ is characterized by its processing requirement (work) $p_j$, its release date $r_j$ and its deadline $d_j$. We are also given a budget…
We prove that the Julia set of a rational function $f$ is computable in polynomial time, assuming that the postcritical set of $f$ does not contain any critical points or parabolic periodic orbits.
This paper presents a novel framework for Jacobian computation in motion optimization problems involving multi-link systems, where physical quantities are represented using higher-order time derivatives. In motion optimization of robots and…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-M\"obius element) to a class of M\"obius semigroups which includes certain settings…
In the dynamic linear program (LP) problem, we are given an LP undergoing updates and we need to maintain an approximately optimal solution. Recently, significant attention (e.g., [Gupta et al. STOC'17; Arar et al. ICALP'18, Wajc STOC'20])…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
We find an abundance of Cremer Julia sets of an arbitrarily high computational complexity.
Many high-dimensional and large-volume data sets of practical relevance have hierarchical structures induced by trees, graphs or time series. Such data sets are hard to process in Euclidean spaces and one often seeks low-dimensional…
In this article, we introduce the adapted inverse iteration method to generate bicomplex Julia sets associated to the polynomial map $w^2+c$. The result is based on a full characterization of bicomplex Julia sets as the boundary of a…
Studying the factorization theory of numerical monoids relies on understanding several important factorization invariants, including length sets, delta sets, and $\omega$-primality. While progress in this field has been accelerated by the…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In…
An algorithm is presented for numerical computation of choreographies in spaces of constant negative curvature in a hyperbolic cotangent potential, extending the ideas given in a companion paper for computing choreographies in the plane in…
We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible, easy to use, and fast. We describe the main design choices…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
Hyperbolic (HB) programming generalizes many popular convex optimization problems, including semidefinite and second-order cone programming. Despite substantial theoretical progress on HB programming, efficient computational tools for…