Related papers: Computable geometric complex analysis and complex …
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
We analyze the infinitesimal effect of holomorphic perturbations of the dynamics of a structurally stable rational map on a neighborhood of its Julia set. This implies some restrictions on the behavior of critical points.
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
It is shown that there is a computable conformal map of the unit disk onto a domain $D$ that has a computable extension to the closure of the unit disk even though the boundary of $D$ is not effectively locally connected. The proof encodes…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
We give a survey on eta invariants including methods of computation and applications in differential topology.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph". Whether or not these fundamental matrices are generically sufficient to recover the global camera configuration…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
Suppose $p \geq 1$ is a computable real. We extend previous work of Clanin, Stull, and McNicholl by classifying the computable $L^p$ spaces whose underlying measure spaces are atomic but not purely atomic. In addition, we determine the…
A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…