Relative Complexity Measure Research Articles

Complexity-Entropy Causality Plane Analysis of Air Pollution Series

In this study, we explore the subtle temporal structure of environmental data using symbolic information-theory approach. The newly developed multivariate multiscale permutation entropy and complexity-entropy causality plane methodology are applied to the six pollutants data recorded in Beijing during 2013–2016, which is a powerful tool to discriminate nonlinear deterministic and stochastic dynamics. The obtained results showed that pollutant series exhibit significant randomness and a lower level of predictability in spring and summer, and more temporal correlations in winter and fall. In addition, surrogate analysis is implemented to avoid biased conclusion. We also define the relative complexity measure of multivariate series to reflect the complexity of a system. The highest relative complexity in winter is in line with the physical behavior of the pollution phenomenon.

Structural Complexity and Informational Transfer in Spatial Log-Gaussian Cox Processes

The doubly stochastic mechanism generating the realizations of spatial log-Gaussian Cox processes is empirically assessed in terms of generalized entropy, divergence and complexity measures. The aim is to characterize the contribution to stochasticity from the two phases involved, in relation to the transfer of information from the intensity field to the resulting point pattern, as well as regarding their marginal random structure. A number of scenarios are explored regarding the Matérn model for the covariance of the underlying log-intensity random field. Sensitivity with respect to varying values of the model parameters, as well as of the deformation parameters involved in the generalized informational measures, is analyzed on the basis of regular lattice partitionings. Both a marginal global assessment based on entropy and complexity measures, and a joint local assessment based on divergence and relative complexity measures, are addressed. A Poisson process and a log-Gaussian Cox process with white noise intensity, the first providing an upper bound for entropy, are considered as reference cases. Differences regarding the transfer of structural information from the intensity field to the subsequently generated point patterns, reflected by entropy, divergence and complexity estimates, are discussed according to the specifications considered. In particular, the magnitude of the decrease in marginal entropy estimates between the intensity random fields and the corresponding point patterns quantitatively discriminates the global effect of the additional source of variability involved in the second phase of the double stochasticity.

Density-based clustering: A 'landscape view' of multi-channel neural data for inference and dynamic complexity analysis.

Two, partially interwoven, hot topics in the analysis and statistical modeling of neural data, are the development of efficient and informative representations of the time series derived from multiple neural recordings, and the extraction of information about the connectivity structure of the underlying neural network from the recorded neural activities. In the present paper we show that state-space clustering can provide an easy and effective option for reducing the dimensionality of multiple neural time series, that it can improve inference of synaptic couplings from neural activities, and that it can also allow the construction of a compact representation of the multi-dimensional dynamics, that easily lends itself to complexity measures. We apply a variant of the ‘mean-shift’ algorithm to perform state-space clustering, and validate it on an Hopfield network in the glassy phase, in which metastable states are largely uncorrelated from memories embedded in the synaptic matrix. In this context, we show that the neural states identified as clusters’ centroids offer a parsimonious parametrization of the synaptic matrix, which allows a significant improvement in inferring the synaptic couplings from the neural activities. Moving to the more realistic case of a multi-modular spiking network, with spike-frequency adaptation inducing history-dependent effects, we propose a procedure inspired by Boltzmann learning, but extending its domain of application, to learn inter-module synaptic couplings so that the spiking network reproduces a prescribed pattern of spatial correlations; we then illustrate, in the spiking network, how clustering is effective in extracting relevant features of the network’s state-space landscape. Finally, we show that the knowledge of the cluster structure allows casting the multi-dimensional neural dynamics in the form of a symbolic dynamics of transitions between clusters; as an illustration of the potential of such reduction, we define and analyze a measure of complexity of the neural time series.

Dependence Assessment Based on Generalized Relative Complexity: Application to Sampling Network Design

Generalized statistical complexity measures provide a means to jointly quantify inner information and relative structural richness of a system described in terms of a probability model. As a natural divergence-based extension in this context, generalized relative complexity measures have been proposed for the local comparison of two given probability distributions. In this paper, the behavior of generalized relative complexity measures is studied for assessment of structural dependence in a random vector leading to a concept of ‘generalized mutual complexity’. A related optimality criterion for sampling network design, which provides an alternative to mutual information based methods in the complexity context, is formulated. Aspects related to practical implementation, and conceptual issues regarding the meaning and potential use of this approach, are discussed. Numerical examples are used for illustration.

Testing robustness of relative complexity measure method constructing robust phylogenetic trees for Galanthus L. using the relative complexity measure.

BackgroundMost phylogeny analysis methods based on molecular sequences use multiple alignment where the quality of the alignment, which is dependent on the alignment parameters, determines the accuracy of the resulting trees. Different parameter combinations chosen for the multiple alignment may result in different phylogenies. A new non-alignment based approach, Relative Complexity Measure (RCM), has been introduced to tackle this problem and proven to work in fungi and mitochondrial DNA.ResultIn this work, we present an application of the RCM method to reconstruct robust phylogenetic trees using sequence data for genus Galanthus obtained from different regions in Turkey. Phylogenies have been analyzed using nuclear and chloroplast DNA sequences. Results showed that, the tree obtained from nuclear ribosomal RNA gene sequences was more robust, while the tree obtained from the chloroplast DNA showed a higher degree of variation.ConclusionsPhylogenies generated by Relative Complexity Measure were found to be robust and results of RCM were more reliable than the compared techniques. Particularly, to overcome MSA-based problems, RCM seems to be a reasonable way and a good alternative to MSA-based phylogenetic analysis. We believe our method will become a mainstream phylogeny construction method especially for the highly variable sequence families where the accuracy of the MSA heavily depends on the alignment parameters.

Inferring Phylogenies from Physico-Chemical Properties of DNA

Phylogenetic analysis relies on alignment of related sequences from different species to obtain the distances between these species. The quality of the alignment and the distance measure would depend on the alignment parameters that are used. In this work, we propose to use Relative Complexity Measure (RCM) method to find the distances between the sequences which is a parameter independent measure. We used DNA sequences from Candida species and phylogenetic trees were obtained using un-weighted pair-group with arithmetic mean method. We used three reduced alphabets for the DNA sequences which were clustered by taking into account different physico-chemical properties of DNA. RCM gives as good results as the distance determination method and among the physico-chemical properties, Keto/Amino grouping is found to give the most accurate tree which is topologically closest to the desired phylogeny.

A generalized relative complexity: Application to atomic one-particle densities

The search of an appropriate measure of relative complexity among density functions is afforded. In doing so, the main properties required for complexity functionals of a given distribution, as well as those for discrimination measures among two or more distributions are considered. A proposal for a generalized relative complexity is provided, enclosing a pioneering definition as a limiting case. A theoretical analysis of the generalized measure for arbitrary distributions is carried out. The applications regard the electron charge densities of neutral atoms, and the results are interpreted on the basis of the main physical properties of the systems considered.

A novel approach for complexity measure analysis in design projects

This study report presents a graph-based model to measure the relative complexity of design projects. Using managerial and technical graphs and complexity design structure matrix, the relative complexity of design projects can be determined. The relative complexity measure can support assembly-oriented design, and guide the designer in creating a product with the most effective balance of manufacturing and assembly complexity. Furthermore, the complexity measures can be used as a yardstick for budgeting and resource allocation for future design projects or maintenance cost estimation. An illustrative example is demonstrated to present the application of the model.

Editorial: engineering approaches to study cardiovascular physiology: modeling, estimation, and signal processing

EDITORIAL article Front. Physiol., 05 November 2012Sec. Computational Physiology and Medicine Volume 3 - 2012 | https://doi.org/10.3389/fphys.2012.00425

Defining statistical relative complexity measure: Application to diversity in atoms

A statistical relative complexity measure, based on the Kullback–Leibler distance measure defining the relative information and the Carbó quantum similarity index defining the relative disequilibrium is proposed. It is shown that with the specific choice of prior density corresponding to the atom at the beginning of the subshell, this measure reveals the diversity of atoms as the subshells are filled across the periodic table. Numerical tests are reported using the non-relativistic Hartree–Fock as well as the relativistic Dirac–Fock density for all atoms in the periodic table.

A generalized relative complexity measure

A class of two-parameter relative complexity measures is presented. Severalimportant properties are proved. As an example we consider the Dicke modelthat describes a single-mode bosonic field interacting with an ensemble ofN two-level atoms. There is a quantum phase transition in the limit. It is found that the relative complexity is an excellent marker of the quantum phasetransition.

Using a Delphi process and the Analytic Hierarchy Process (AHP) to evaluate the complexity of projects

Project complexity is ever growing and needs to be understood, analysed and measured better to assist modern project management. The overall ambition of this paper is therefore to define a measure of project complexity in order to assist decision-making, notably when analysing several projects in a portfolio, or when studying different areas of a project. A synthesised literature review on existing complexity measures is firstly proposed in order to highlight their limitations. Then, we identify the multiple aspects of project complexity thanks to the construction and refinement of a project complexity framework thanks to an international Delphi study. We then propose a multi-criteria approach to project complexity evaluation, underlining the benefits of such an approach. In order to solve properly this multi-criteria problem, we first conduct a critical state of the art on multi-criteria methodologies. We then argue for the use of the Analytic Hierarchy Process. In the end, this tool permits to define a relative project complexity measure, which can notably assist decision-making. Complexity scales and subscales are defined in order to highlight the most complex alternatives and their principal sources of complexity within the set of criteria and sub-criteria which exist in the hierarchical structure. Finally, a case study within a start-up firm in the entertainment industry (musicals production) is performed. Conclusions, limitations and perspectives of research are given in the end.

Predictive Space Weather: An information theory approach

It is rather well recognized that the global dynamics of the Sun–Earth relationship involves complex nonlinear phenomena. Here we present a preliminary attempt to characterize the influence and the timing of the solar magnetic activity on the near-Earth environment, based on quite novel tools based on concepts from information theory. In detail, we show two preliminary examples. In the first one, we investigate the time behaviour of the delayed mutual information applied to the solar wind forcing on ionospheric irregularities in a stormy period of November 2004; in the other example, we study the evolution of a possible measure of relative complexity for the diurnal variability of the vertical total electron content during the “Halloween Storm” of year 2003. The future use of data from the Galileo system will give a definitive improvement to the application of such techniques to Space Weather.

Measuring project complexity using the Analytic Hierarchy Process

Project complexity is ever growing and needs to be understood and measured better to assist modern project management. The overall ambition of this paper is therefore to define a measure of project complexity in order to assist decision-making. A synthesised literature review on existing complexity measures is proposed in order to highlight their limitations. Then, we identify the multiple aspects of project complexity. We then propose a multi-criteria approach to project complexity evaluation, through the use of the Analytic Hierarchy Process. In the end, it permits to define a relative project complexity measure. Complexity scales and subscales are defined in order to highlight the most complex alternatives and their principal sources of complexity within the set of criteria and sub-criteria which exist in the hierarchical structure. Finally, a case study within a start-up firm in the entertainment industry is performed. Conclusions and research perspectives are given in the end.

Clustering of protein families into functional subtypes using Relative Complexity Measure with reduced amino acid alphabets

BackgroundPhylogenetic analysis can be used to divide a protein family into subfamilies in the absence of experimental information. Most phylogenetic analysis methods utilize multiple alignment of sequences and are based on an evolutionary model. However, multiple alignment is not an automated procedure and requires human intervention to maintain alignment integrity and to produce phylogenies consistent with the functional splits in underlying sequences. To address this problem, we propose to use the alignment-free Relative Complexity Measure (RCM) combined with reduced amino acid alphabets to cluster protein families into functional subtypes purely on sequence criteria. Comparison with an alignment-based approach was also carried out to test the quality of the clustering.ResultsWe demonstrate the robustness of RCM with reduced alphabets in clustering of protein sequences into families in a simulated dataset and seven well-characterized protein datasets. On protein datasets, crotonases, mandelate racemases, nucleotidyl cyclases and glycoside hydrolase family 2 were clustered into subfamilies with 100% accuracy whereas acyl transferase domains, haloacid dehalogenases, and vicinal oxygen chelates could be assigned to subfamilies with 97.2%, 96.9% and 92.2% accuracies, respectively.ConclusionsThe overall combination of methods in this paper is useful for clustering protein families into subtypes based on solely protein sequence information. The method is also flexible and computationally fast because it does not require multiple alignment of sequences.

A graph-based model for manufacturing complexity

This paper presents a graph-based model to measure the relative manufacturing complexity of and the manufacturing similarity of products in job shop manufacturing systems. This model depicts the impact of the complexity factors on the profit realisable from products based on their manufacturing process and required resources/skills. These resources deal with the process required for a component to reach assembly, the process of assembling the components to a whole product. This relative manufacturing complexity measure not only can support assembly and production cost estimation, but also can provide a guideline for creating a product with the most effective balance of manufacturing and assembly. Also, the results of this study can help improve budgeting and resource allocation, and the product life cycle cost estimation for future products. A numerical example is also presented to demonstrate the application of the proposed approach.

Structural complexity of disordered surfaces: Analyzing the porous silicon SFM patterns

This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the structural complexity of disordered surfaces (and interfaces) observed and/or simulated in nano, micro and ordinary scales.

A matching pursuit-based signal complexity measure for the analysis of newborn EEG

This paper presents a new relative measure of signal complexity, referred to here as relative structural complexity (RSC), which is based on the matching pursuit (MP) decomposition. By relative, we refer to the fact that this new measure is highly dependent on the decomposition dictionary used by MP. The structural part of the definition points to the fact that this new measure is related to the structure, or composition, of the signal under analysis. After a formal definition, the proposed RSC measure is used in the analysis of newborn electroencephalogram (EEG). To do this, firstly, a time-frequency decomposition dictionary is specifically designed to compactly represent the newborn EEG seizure state using MP. We then show, through the analysis of synthetic and real newborn EEG data, that the relative structural complexity measure can indicate changes in EEG structure as it transitions between the two EEG states; namely seizure and background (non-seizure).

Dispatch sequences for embedded control models

We consider the problem of mapping a set of control components to an executable implementation. The standard approach to this problem involves mapping control blocks to periodic tasks, and then generating a schedule. This schedule is platform-dependent, and its execution requires real-time operating system support. We propose an alternative approach which involves generating a dispatch sequence of control blocks in a platform-independent manner. Our solution relies on assigning relative complexity and relative importance measures to control components, and is an adaptation of the classical scheduling algorithms such as earliest–deadline–first. We show the benefits of our approach using simulation experiments on two case studies.

Antlers honestly advertise sperm production and quality

Evolutionary theory proposes that exaggerated male traits have evolved via sexual selection, either through female mate choice or male-male competition. While female preferences for ornamented males have been amply demonstrated in other taxa, among mammals sexual characters are commonly regarded as weapons whose main function is to enhance male competitiveness in agonistic encounters. One particularly controversial hypothesis to explain the function of male sexual characters proposes that they advertise male fertility. We test this hypothesis in red deer (Cervus elaphus), a species where sexual characters (antlers) reach an extreme degree of elaboration. We find that a global measure of relative antler size and complexity is associated with relative testes size and sperm velocity. Our results exclude the possibility that condition dependence, age or time of culling, drive these associations. Red deer antlers could signal male fertility to females, the ability to avoid sperm depletion throughout the reproductive season and/or the competitive ability of ejaculates. By contrast, male antlers could also signal to other males not only their competitive ability at the behavioural level (fighting ability) but also at the physiological level (sperm competition).