Towards a Universal Measure of Complexity

Gradistics: An underappreciated dimension in evolutionary space

The growth of complexity is an unsolved and underappreciated problem. We consider possible causes of this growth, hypotheses testing, molecular mechanisms, complexity measures, cases of simplification, and significance for biomedicine. We focus on a general ability of regulation, which is based on the growing information storage and processing capacities, as the main proxy of complexity. Natural selection is indifferent to complexity. However, complexification can be inferred from the same first principle, on which natural selection is founded. Natural selection depends on potentially unlimited reproduction under limited environmental conditions. Because of the demographic pressure, the simple ecological niches become fulfilled and diversified (due to species splitting and divergence). Diversification increases complexity of biocenoses. After the filling and diversification of simple niches, the more complex niches can arise. This is the 'atomic orbitals' (AO) model. Complexity has many shortcomings but it has an advantage. This advantage is ability to regulatory adaptation, including behavioral, formed in the evolution by means of genetic adaptation. Regulatory adaptation is much faster than genetic one because it is based on the information previously accumulated via genetic adaptation and learning. Regulatory adaptation further increases complexity of biocenoses. This is the 'regulatory advantage' (RA) model. The comparison of both models allows testable predictions. We focus on the animal evolution because of the appearance of higher regulatory level (nervous system), which is absent in other lineages, and relevance to humans (including biomedical aspects).

Three Decades in Econophysics—From Microscopic Modelling to Macroscopic Complexity and Back

We explore recent contributions to research in Econophysics, switching between Macroscopic complexity and microscopic modelling, showing how each leads to the other and detailing the everyday applicability of both approaches and the tools they help develop. Over the past decades, the world underwent several major crises, leading to significant increase in interdependence and, thus, complexity. We show here that from the perspective of network science, these processes become more understandable and, to some extent, also controllable.

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions-as a function of time series length-present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.

Complexity in Economic and Social Systems

During recent years we have witnessed a systematic progress in the understanding of complex systems, both in the case of particular systems that are classified into this group and, in general, as regards the phenomenon of complexity [...].

Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19

Social systems are characterized by an enormous network of connections and factors that can influence the structure and dynamics of these systems. Among them the whole economical sphere of human activity seems to be the most interrelated and complex. All financial markets, including the youngest one, the cryptocurrency market, belong to this sphere. The complexity of the cryptocurrency market can be studied from different perspectives. First, the dynamics of the cryptocurrency exchange rates to other cryptocurrencies and fiat currencies can be studied and quantified by means of multifractal formalism. Second, coupling and decoupling of the cryptocurrencies and the conventional assets can be investigated with the advanced cross-correlation analyses based on fractal analysis. Third, an internal structure of the cryptocurrency market can also be a subject of analysis that exploits, for example, a network representation of the market. In this work, we approach the subject from all three perspectives based on data from a recent time interval between January 2019 and June 2020. This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.