javaPlex: A Research Software Package for Persistent (Co)Homology

Adams, Henry; Tausz, Andrew; Vejdemo-Johansson, Mikael

doi:10.1007/978-3-662-44199-2_23

Cited by 144 publications

(107 citation statements)

References 4 publications

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“…We now consider the subspace P ⊆ F, consisting of all functions within F which have the form c(ax + by) 2 Each restriction of h m (m = 3, 4, 5, 6, 7) to the subspace P of F is one-to-one.…”

Section: Klein Bottle and A Space Of Degree 2 Polynomialsmentioning

confidence: 99%

A topological analysis of high-contrast patches in natural images

Xia¹

2016

J. Nonlinear Sci. Appl.

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In this paper, we study qualitative topological analysis of spaces of natural images locally. We apply the techniques of computational topology to the space of 3 × 3, 4 × 4, 5 × 5, 6 × 6 and 7 × 7 high-contrast patches. We show that in each case there is a subspace of the space of all high-contrast patches that is topologically equivalent to the Klein bottle and we found that the size of the largest subspace having the Klein bottle's homology decreases with increasing of the size of patches. The data sets used in this paper are different from that discussed in the paper "on the local behavior of spaces of natural images", we conformed our findings by applying the same methods to the different sizes patches. c ⃝2016 All rights reserved.

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Section: Klein Bottle and A Space Of Degree 2 Polynomialsmentioning

confidence: 99%

A topological analysis of high-contrast patches in natural images

Xia¹

2016

J. Nonlinear Sci. Appl.

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“…De Silva and Carlsson in [14] discover r = 0 to be generally less effective and r = 2 has the disadvantage of connecting every landmark point to at least one other at R = 0. Please refer to the papers [3,6,14,19] for more details about lazy witness complexes and persistent homology.…”

Section: Persistent Homologymentioning

confidence: 99%

A topological analysis on patches of optical flow

Xia¹

2016

J. Nonlinear Sci. Appl.

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The research of optical flow is vitally important topic in computer vision. In this paper we research a topological analysis of space of optical flow locally. We use the methods of computing topology to the spaces of 4 × 4 and 6 × 6 high contrast optical flow patches. We experimentally prove that in both cases there exist subspaces of the spaces of all high contrast optical flow patches that is topologically equivalent to a circle, which states that some results on the topological analysis of natural images and range images can be extended to the scope of image motion.

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“…The computational algorithms for the characterization of simplicial complexes require as input a filtered simplicial complex, i.e., a simplicial complex equipped with a filter value. A filter value [22] can be considered as a time-appearing value along the process described below. The set of obtained filter values is called the filter set and must be a strictly ordered set.…”

Section: From Weighted Graphs To Filtered Simplicial Complexesmentioning

confidence: 99%

Topological Characterization of Complex Systems: Using Persistent Entropy

Merelli

Rucco

Sloot

et al. 2015

Entropy

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In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly-introduced quantitative concept of persistent entropy, and it is described by a persistent entropy automaton. The other level, the behavioral B one, is characterized by a network of interacting computational agents. The presented methodology is applied to a real case study, the idiotypic network of the mammalian immune system.

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javaPlex: A Research Software Package for Persistent (Co)Homology

Cited by 144 publications

References 4 publications

A topological analysis of high-contrast patches in natural images

A topological analysis of high-contrast patches in natural images

A topological analysis on patches of optical flow

Topological Characterization of Complex Systems: Using Persistent Entropy

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