Counterexamples for Topological Complexity in Digital Images

Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a topological space. We indicate that the results on topological complexities of certain path-connected topological spaces show alterations in digital images. We also give a result about the digital topological complexity number using the genus of a digital surface in discrete geometry

Chinese Internet AS-level Topology

We present the first complete measurement of the Chinese Internet topology at the autonomous systems (AS) level based on traceroute data probed from servers of major ISPs in mainland China. We show that both the Chinese Internet AS graph and the global Internet AS graph can be accurately reproduced by the Positive-Feedback Preference (PFP) model with the same parameters. This result suggests that the Chinese Internet preserves well the topological characteristics of the global Internet. This is the first demonstration of the Internet's topological fractality, or self-similarity, performed at the level of topology evolution modeling.Comment: This paper is a preprint of a paper submitted to IEE Proceedings on Communications and is subject to Institution of Engineering and Technology Copyright. If accepted, the copy of record will be available at IET Digital Librar

On some uses and abuses of topology in the social analysis of technology (Or the problem with smart meters)

This article examines different ways in which topological ideas can be used to analyse technology in social terms, arguing that we must become more discerning and demanding as to the limits and possibilities of topological analysis than used to be necessary. Topological framings of technology and society are increasingly widespread, and in this context, it becomes necessary to consider topology not just as a theory to be adopted, but equally as a device that is deployed in social life in a variety of ways. Digital technologies require special attention in this regard: on the one hand, these technologies have made it possible for a topological imagination of technology and society to become more widely adopted; on the other hand, they have also enabled a weak form of topological imagination to proliferate, one that leaves in place old, deterministic ideas about technology as a principal driver of social change. Turning to an empirical case, that of smart electricity metering, the article investigates how topological approaches enable both limited and rigorous ‘expansions of the frame’ on technology. In some cases, topology is used to imagine technology as a dynamic, heterogeneous arrangement, but ‘the primacy of technology’ is maintained. In other cases a topological approach is used to bring into view much more complex relations between technological and societal change. The article ends with an exploration of the topological devices that are today deployed to render relations between technological and social change more complexly, such as the online visualisation tool of tag clouding. I propose that such a topological device enables an empirical mode of critique: here, topology does not just help to make the point of the mutual entanglement of the social and the technical, but helps to dramatize the contingent, dynamic and non-coherent unfolding of issues

Beyond the Hausdorff metric in digital topology

[EN] Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar geometric or topological property. Such measures may be combined with the Hausdorff metric to yield a metric in which close images are similar with respect to multiple properties.Boxer, L. (2022). Beyond the Hausdorff metric in digital topology. Applied General Topology. 23(1):69-77. https://doi.org/10.4995/agt.2022.15893697723

2D parallel thinning and shrinking based on sufficient conditions for topology preservation

Thinning and shrinking algorithms, respectively, are capable of extracting medial lines and topological kernels from digital binary objects in a topology preserving way. These topological algorithms are composed of reduction operations: object points that satisfy some topological and geometrical constraints are removed until stability is reached. In this work we present some new sufficient conditions for topology preserving parallel reductions and fiftyfour new 2D parallel thinning and shrinking algorithms that are based on our conditions. The proposed thinning algorithms use five characterizations of endpoints