Related papers: Computability of finite simplicial complexes
The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial…
Suppose we are given a computably enumerable object arise from algorithmic randomness or computable analysis. We are interested in the strength of oracles which can compute an object that approximates this c.e. object. It turns out that,…
We show that there are Turing complete computably enumerable sets of arbitrarily low non-trivial initial segment prefix-free complexity. In particular, given any computably enumerable set $A$ with non-trivial prefix-free initial segment…
Through careful analysis of types inspired by [AGTW21] we characterize a notion of definable compactness for definable topologies in general o-minimal structures, generalizing results from [PP07] about closed and bounded definable sets in…
Bipartite Graph is often a realistic model of complex networks where two different sets of entities are involved and relationship exist only two entities belonging to two different sets. Examples include the user-item relationship of a…
Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular,…
The concept of well group in a special but important case captures homological properties of the zero set of a continuous map $f:K\to R^n$ on a compact space K that are invariant with respect to perturbations of f. The perturbations are…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected…
A computable graph $\mathcal{G}$ is computably categorical relative to a degree $\mathbf{d}$ if and only if for all $\mathbf{d}$-computable copies $\mathcal{B}$ of $\mathcal{G}$, there is a $\mathbf{d}$-computable isomorphism…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
We provide requirements on effectively enumerable topological spaces which guarantee that the Rice-Shapiro theorem holds for the computable elements of these spaces. We show that the relaxation of these requirements leads to the classes of…
Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hypergraphs -- specifically simplicial, relative, and chain…
ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated…
Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…