On the Metric Topology Induced from the BIC-based Consistent Metric between Markovian Processes
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In recent papers (see reference list) the authors Garcia, Gholizadeh and Gonzalez-Lopez develop a local metric from a distance measure between samples coming from discrete Markovian processes. This metric is associated to the Bayesian Information Criterion (BIC). They use the metric to decide if 2 independent samples are governed by the same Stochastic Law. Their results are applied to many topics, including internet navigation patterns, lines of production and Zika strains, for example. In this paper we expand on the measure above by examining the metric (topological) space induced by it. For instance, we exhibit the open sets in this topology, which are of course the unions of open balls under the metric. We then look at the bases for this topology and check for other topological properties. We show that the metric space cannot be compact and later form an identification space. We conclude by interpreting the work of the authors above in the topological context as well as providing other applications and results, e.g. to other vector-borne diseases and to the DNA molecule.
Abstract
In recent papers (see reference list) the authors Garcia, Gholizadeh and Gonzalez-Lopez develop a local metric from a distance measure between samples coming from discrete Markovian processes. This metric is associated to the Bayesian Information Criterion (BIC). They use the metric to decide if 2 independent samples are governed by the same Stochastic Law. Their results are applied to many topics, including internet navigation patterns, lines of production and Zika strains, for example. In this paper we expand on the measure above by examining the metric (topological) space induced by it. For instance, we exhibit the open sets in this topology, which are of course the unions of open balls under the metric. We then look at the bases for this topology and check for other topological properties. We show that the metric space cannot be compact and later form an identification space. We conclude by interpreting the work of the authors above in the topological context as well as providing other applications and results, e.g. to other vector-borne diseases and to the DNA molecule.
참고문헌 (10)
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- Jesús Enrique García, "Partition Markov Model for Covid-19 Virus", 4open, 3, pp.13~ (2020), EDP Sciences[DOI]
- Bozeman JR, "More Genus-One Whitehead Manifolds and Counterexamples to a Con-jecture of Brown", Proc. Jangjeon Math. Soc, 9, pp.1~7 (2006)
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