The dawn of the RNA World:toward functional complexity through ligation of random RNA oligomers

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation- based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered. Copyright © 2009 RNA Society.

Statnote 34 : the Kolmogorov-Smirnov (KS) test

The Kolmogorov-Smirnov (KS) test is a non-parametric test which can be used in two different circumstances. First, it can be used as an alternative to chi-square (?2) as a ‘goodness-of-fit’ test to compare whether a given ‘observed’ sample of observations conforms to an ‘expected’ distribution of results (KS, one-sample test). An example of the use of the one-sample test to determine whether a sample of observations was normally distributed was described previously. Second, it can be used as an alternative to the Mann-Whitney test to compare two independent samples of observations (KS, two-sample test). Hence, this statnote describes the use of the KS test with reference to two scenarios: (1) to compare the observed frequency (Fo) of soil samples containing cysts of the protozoan Naegleria collected each month for a year with an expected equal frequency (Fe) across months (one-sample test), and (2) to compare the abundance of bacteria on cloths and sponges sampled in a domestic kitchen environment (two-sample test).

Prediction, volatility and complexity of financial markets:a move-based approach

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Complexity analysis of electroencephalographic data

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Complexity measures of electroencephalographic data

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Individual differences in cognitive style:preference for complexity-simplicity

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Changes in neural complexity during the perception of 3D images using random dot stereograms

One developing theme in consciousness research is that consciousness is not the product of any specific component of the brain, rather it is an emergent property of the changing patterns of connectivity between different specialised functional components. For example, the dynamic core hypothesis proposes that conscious experience requires high levels of neural complexity, where complexity is defined in terms of functional connectivity. To test this hypothesis, electroencephalography was recorded while participants were shown random dot-stereograms. Consistent with the dynamic core hypothesis, neural complexity increased as the participants changed from simply viewing the stereogram to consciously perceiving the hidden 3D image.

Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system. © 2004 Wiley Periodicals, Inc.

Dynamic complexity of chaotic transitions in high-dimensional classical dynamics:Leu-Enkephalin folding

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A ß-turn transition is investigated by calculating the topological complexity (in the "computational mechanics" framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the ß-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a "quasi-regular" dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated. © Springer-Verlag Berlin Heidelberg 2006.

Measuring complexity through average symmetry

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures

Complexity of classical dynamics of molecular systems. I. Methodology

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. “Computational mechanics” is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Enhancing the performance of intelligent control systems in the face of higher levels of complexity and uncertainty

Modern advances in technology have led to more complex manufacturing processes whose success centres on the ability to control these processes with a very high level of accuracy. Plant complexity inevitably leads to poor models that exhibit a high degree of parametric or functional uncertainty. The situation becomes even more complex if the plant to be controlled is characterised by a multivalued function or even if it exhibits a number of modes of behaviour during its operation. Since an intelligent controller is expected to operate and guarantee the best performance where complexity and uncertainty coexist and interact, control engineers and theorists have recently developed new control techniques under the framework of intelligent control to enhance the performance of the controller for more complex and uncertain plants. These techniques are based on incorporating model uncertainty. The newly developed control algorithms for incorporating model uncertainty are proven to give more accurate control results under uncertain conditions. In this paper, we survey some approaches that appear to be promising for enhancing the performance of intelligent control systems in the face of higher levels of complexity and uncertainty.

A question of complexity:measuring the maturity of online enquiry communities

Online enquiry communities such as Question Answering (Q&A) websites allow people to seek answers to all kind of questions. With the growing popularity of such platforms, it is important for community managers to constantly monitor the performance of their communities. Although different metrics have been proposed for tracking the evolution of such communities, maturity, the process in which communities become more topic proficient over time, has been largely ignored despite its potential to help in identifying robust communities. In this paper, we interpret community maturity as the proportion of complex questions in a community at a given time. We use the Server Fault (SF) community, a Question Answering (Q&A) community of system administrators, as our case study and perform analysis on question complexity, the level of expertise required to answer a question. We show that question complexity depends on both the length of involvement and the level of contributions of the users who post questions within their community. We extract features relating to askers, answerers, questions and answers, and analyse which features are strongly correlated with question complexity. Although our findings highlight the difficulty of automatically identifying question complexity, we found that complexity is more influenced by both the topical focus and the length of community involvement of askers. Following the identification of question complexity, we define a measure of maturity and analyse the evolution of different topical communities. Our results show that different topical communities show different maturity patterns. Some communities show a high maturity at the beginning while others exhibit slow maturity rate. Copyright 2013 ACM.