Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.Comment: 44 pages, 12 figures; made revisions after peer revie

Kolmogorov complexity spectrum for use in analysis of UV-B radiation time series

We have used the Kolmogorov complexity and sample entropy measures to estimate the complexity of the UV-B radiation time series in the Vojvodina region (Serbia) for the period 1990-2007. We defined the Kolmogorov complexity spectrum and have introduced the Kolmogorov complexity spectrum highest value (KLM). We have established the UV-B radiation time series on the basis of their daily sum (dose) for seven representative places in this region using (i) measured data, (ii) data calculated via a derived empirical formula and (iii) data obtained by a parametric UV radiation model. We have calculated the Kolmogorov complexity (KL) based on the Lempel-Ziv Algorithm (LZA), KLM and Sample Entropy (SE) values for each time series. We have divided the period 1990-2007 into two sub-intervals: (a) 1990-1998 and (b)1999-2007 and calculated the KL, KLM and SE values for the various time series in these sub-intervals. It is found that during the period 1999-2007, there is a decrease in the KL, KLM and SE, comparing to the period 1990-1998. This complexity loss may be attributed to (i) the increased human intervention in the post civil war period causing increase of the air pollution and (ii) the increased cloudiness due to climate changes.Comment: 10 pages, 1 figure, 1 table. arXiv admin note: substantial text overlap with arXiv:1301.2039; This paper has been accepted in Modern Physics Letters B on Aug 14, 201

Model predictive control scheme for rotorcraft inverse simulation

A novel inverse simulation scheme is proposed for application to rotorcraft dynamic models. The algorithm is based on a model predictive control scheme that allows for a faster solution of the inverse simulation step, working on a lower{order, simplified helicopter model. The control action is then propagated forward in time on a more complete model. The algorithm compensates for discrepancies between the models by means of a simple guidance scheme. The proposed approach allows for the assessment of handling quality potential on the basis of the most sophisticated model, adopted for the forward simulation, while keeping model complexity to a minimum level for the computationally more demanding inverse simulation algorithm. This allows for a faster solution of the inverse problem, if compared with the computational time necessary for solving the same problem on the basis of the full{order, more complex model. At the same time, the results are not a�ected by modeling approximations at the basis of the simpli�ed one. The reported results, for an articulated blade, single main rotor helicopter model demonstrate the validity of the approach