Observability of Complex Systems by Means of Relative Distances Between Homological Groups

Juan G Diaz Ochoa

doi:10.3389/fphy.2020.465982

Abstract

It is common to consider using a data-intensive strategy as a way to develop systemic and quantitative analysis of complex systems so that data collection, sampling, standardization, visualization, and interpretation can determine how causal relationships are identified and incorporated into mathematical models. Collecting enough large datasets seems to be a good strategy in reducing bias of the collected data; but persistent and dynamic anomalies in the data structure, generated from variations in intrinsic mechanisms, can actually induce persistent entropy thus affecting the overall validity of quantitative models. In this research, we are introducing a method based on the definition of homological groups that aims at evaluating this persistent entropy as a complexity measure to estimate the observability of the systems. This method identifies patterns with persistent topology, extracted from the combination of different time series and clustering them to identify persistent bias in the data. We tested this method on accumulated data from patients using mobile sensors to measure the response of physical exercise in real-world conditions outside the lab. With this method, we aim to better stratify time series and customize models in complex biological systems.

Highlights

The quantitative description of complex systems often makes use of time series because its relationships and correlations aim to infer causal connections between observations [1]
We face the problem of estimating persistent entropy generated by all the internal processes and states in complex systems that could compromise the stability of a quantitative description of a complex system
The quantitative description of complex systems is limited from the internal states of the system from accessible data, which is in practice limited to a subset of variables

Summary

Introduction

The quantitative description of complex systems often makes use of time series because its relationships and correlations aim to infer causal connections between observations [1]. Previous research has focused on the definition of causality tests by using time series [1], for example, using transfer entropy [2]. Causality inference can be complicated by a bias when estimating a limited amount of data that is possibly noisy [1]. This causality inference is based on the notion of cooperative behavior of complex coupled systems, where synchronization and related phenomena have been observed, for example, in physical and biological systems [4]

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Methods

Discussion

Conclusion