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Learning Topology: Bridging Computational Topology and Machine Learning [PDF]

Pattern Recognition and Image Analysis, 2021
Topology is a classical branch of mathematics, born essentially from Euler's studies in the XVII century, which deals with the abstract notion of shape and geometry. Last decades were characterised by a renewed interest in topology and topology-based tools, due to the birth of computational topology and Topological Data Analysis (TDA).
Maria Antonietta Pascali, Davide Moroni, Pascali Maria Antonietta   +2 more
exaly   +5 more sources

Computational Topology in Text Mining [PDF]

Lecture Notes in Computer Science, 2012
In this paper we present our ongoing research on applying computational topology to analysis of structure of similarities within a collection of text documents. Our work is on the fringe between text mining and computational topology, and we describe techniques from each of these disciplines.
Pawel Dlotko, Marian Mrózek, Hubert Wagner   +2 more
exaly   +3 more sources

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Some Results in Computational Topology

Journal of the ACM, 1972
It is the object of this paper to study the topological properties of finite graphs that can be embedded in the n -dimensional integral lattice (denoted N n ). The basic notion of deletability of a node is first introduced.
George Tourlakis, John Mylopoulos
openaire   +2 more sources

Computable Topology for Reliable Computations

2019
Using the framework of computable topology we investigate computable minimality of lifted domain presentations of computable Polish spaces, in particular the real numbers, the Cantor and Baire spaces, the continuous functions on a compact interval, which are widely used in theoretical computer science, e.g., automata theory, computable analysis and ...
Margarita V. Korovina, Oleg V. Kudinov
openaire   +1 more source

Topological Quantum Computation

1999
Following a suggestion of A. Kitaev, we explore the connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions. A suitably designed spin system can support localized excitations (quasiparticles) that exhibit long-range nonabelian Aharonov-Bohm interactions.
Ogburn, R. Walter, Preskill, John
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The Topological Structures of Membrane Computing

Fundamenta Informaticae, 2002
In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes.
Jean-Louis Giavitto, Olivier Michel 0001
openaire   +3 more sources

Topology for Computations of Concurrent Automata

International Journal of Algebra and Computation, 1998
We generalize the results on α-complex traces from [14, 16] to the realm of concurrent automata. We show that the α-complex computations can be defined as elements of a compact, totally disconnected and complete topological semigroup containing the finite computations as a dense and discrete subspace. But in this semigroup it is not possible to define
Dietrich Kuske, R. M. Shortt
openaire   +2 more sources

Outline of Partial Computability in Computable Topology

2017
In the framework of computable topology we investigate properties of partial computable functions, in particular complexity of various problems in computable analysis in terms of index sets, the effective Borel and Lusin hierarchies.
Margarita V. Korovina, Oleg V. Kudinov
openaire   +1 more source