Computationally Tractable Pairwise Complexity Profile

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the information to describe a system as a function of the scale at which it is observed. We present a new formulation of the complexity profile, which expands its possible application to high-dimensional real-world and mathematically defined systems. The new method is constructed from the pairwise dependencies between components of the system. The pairwise approach may serve as both a formulation in its own right and a computationally feasible approximation to the original complexity profile. We compare it to the original complexity profile by giving cases where they are equivalent, proving properties common to both methods, and demonstrating where they differ. Both formulations satisfy linear superposition for unrelated systems and conservation of total degrees of freedom (sum rule). The new pairwise formulation is also a monotonically non-increasing function of scale. Furthermore, we show that the new formulation defines a class of related complexity profile functions for a given system, demonstrating the generality of the formalism.Comment: 18 pages, 3 figure

Multi-Scale Entropy Analysis as a Method for Time-Series Analysis of Climate Data

Evidence is mounting that the temporal dynamics of the climate system are changing at the same time as the average global temperature is increasing due to multiple climate forcings. A large number of extreme weather events such as prolonged cold spells, heatwaves, droughts and floods have been recorded around the world in the past 10 years. Such changes in the temporal scaling behaviour of climate time-series data can be difficult to detect. While there are easy and direct ways of analysing climate data by calculating the means and variances for different levels of temporal aggregation, these methods can miss more subtle changes in their dynamics. This paper describes multi-scale entropy (MSE) analysis as a tool to study climate time-series data and to identify temporal scales of variability and their change over time in climate time-series. MSE estimates the sample entropy of the time-series after coarse-graining at different temporal scales. An application of MSE to Central European, variance-adjusted, mean monthly air temperature anomalies (CRUTEM4v) is provided. The results show that the temporal scales of the current climate (1960–2014) are different from the long-term average (1850–1960). For temporal scale factors longer than 12 months, the sample entropy increased markedly compared to the long-term record. Such an increase can be explained by systems theory with greater complexity in the regional temperature data. From 1961 the patterns of monthly air temperatures are less regular at time-scales greater than 12 months than in the earlier time period. This finding suggests that, at these inter-annual time scales, the temperature variability has become less predictable than in the past. It is possible that climate system feedbacks are expressed in altered temporal scales of the European temperature time-series data. A comparison with the variance and Shannon entropy shows that MSE analysis can provide additional information on the statistical properties of climate time-series data that can go undetected using traditional method

Development of an Approach for Analyzing Supply Chain Complexity

Supply chains are faced with a rising complexity of products, structures, and processes. Because of the strong link between a supply chain’s complexity and its efficiency the supply chain complexity management becomes a major challenge of today’s business management. A two dimensional driver concept is introduced and explained to comprehend the major causes of a supply chains’ complexity. To map the effects of the drivers and to understand the different dimensions of complexity, a general complexity model is introduced. A supply chain complexity analysis approach is presented, to evaluate the initial situation and to provide the necessary information for deriving the right actions and strategies for the management of complexity within a supply chain.complexity; supply chain; variety; model

Towards a measure for characterizing the informational content of audio signals and the relation between complexity and auditory encoding

The accurate description of a complex process should take into account not only the interacting elements involved but also the scale of the description. Therefore, there can not be a single measure for describing the associated complexity of a process nor a single metric applicable in all scenarios. This article introduces a framework based on multiscale entropy to characterize the complexity associated with the most identifiable characteristic of songs: the melody. We are particularly interested in measuring the complexity of popular songs and identifying levels of complexity that statistically explain the listeners’ preferences. We analyze the relationship between complexity and popularity using a database of popular songs and their relative position in a preferences ranking. There is a tendency toward a positive association between complexity and acceptance (success) of a song that is, however, not significant after adjusting for multiple testing.Peer ReviewedPostprint (published version

Distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations.Centro de Investigaciones Óptica

Practical Measurement of Complexity in Dynamic Systems

A difficulty in complexity theory is lack of a clear definition for complexity, particularly one that is measurable. Those approaches that provide measurable definitions for the absolute complexity of a system often impose the requirement of perfect or near-perfect knowledge of system structure.In practice, it is intractable or impossible to measure the complexity of most dynamic systems.However, by measuring behavioral complexity in context with environmental scenarios, it is ossible to set bounds on a system\u27s absolute (maximum) complexity and estimate its total complexity. As this paper shows, behavioral complexity can be determined by observing a system\u27s changes in kinetic energy.This research establishes a methodology for measuring complexity in dynamic systems without the requirement of system structure knowledge. This measurement can be used to compare systems, understand system risks, determine failure dynamics, and guide system architecture