Open AccessBook
Metric Spaces: Iteration and Application
TLDR
In this paper, an introductory text on metric spaces that is written for students who are as interested in the applications as in the theory is presented, and the reader is expected to have had some exposure to elementary analysis.Abstract:
Here is an introductory text on metric spaces that is the first to be written for students who are as interested in the applications as in the theory. Knowledge of metric spaces is fundamental to understanding numerical methods (for example for solving differential equations) as well as analysis, yet most books at this level emphasise just the abstraction and theory. Dr Bryant uses applications to provide motivation and to sustain the development and discusses numerical procedures where appropriate. The reader is expected to have had some exposure to elementary analysis, but the author provides examples throughout to refresh the student's memory and to test and extend understanding. In short, this is an introductory textbook that will appeal to students of mathematics and engineering and will give them the required background for more advanced courses in both analysis and numerical analysis.read more
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Journal ArticleDOI
Useful metrics for modular robot motion planning
TL;DR: The technique of simulated annealing is used to drive the reconfiguration process with configuration metrics as cost functions, and concepts of distance between metamorphic robot configurations are defined, and shown to satisfy the formal properties of a metric.
Book
Digital geometry
Azriel Rosenfeld,Reinhard Klette +1 more
TL;DR: Questions of particular interest include how images and image subsets are digitized; how geometric properties are defined for digitized sets; the computational complexity of computing them--in particular, whether they can be computed using simple (e.g., local) operations; characterizing image operations that preserve them; and characterizing digital objects that could be the digitizations of real objects that have given geometric properties.
Proceedings ArticleDOI
Deep Variational Network Embedding in Wasserstein Space
TL;DR: The experimental results demonstrate that the proposed Deep Variational Network Embedding in Wasserstein Space (DVNE) can effectively model the uncertainty of nodes in networks, and show a substantial gain on real-world applications such as link prediction and multi-label classification compared with the state-of-the-art methods.
Journal ArticleDOI
A New Metric for Grey-Scale Image Comparison
TL;DR: A new grey-scale measure, Δg, aiming to improve upon the most commongrey-scale error measure, the root-mean-square error, is introduced, an extension of the authors' recently developed binary error measure Δb, not only in structure, but also having both a theoretical and intuitive basis.
Journal ArticleDOI
ClusterJoin: a similarity joins framework using map-reduce
TL;DR: A ClusterJoin framework that partitions the data space based on the underlying data distribution, and distributes each record to partitions in which they may produce join results based onThe distance threshold, and develops a dynamic load balancing scheme using sampling, which provides strong probabilistic guarantees on the size of partitions, and greatly improves scalability.