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.

Rational design of heterogeneous catalysts for biodiesel synthesis

Dwindling oil reserves and growing concerns over carbon dioxide emissions and associated climate change are driving the utilisation of renewable feedstocks as alternative, sustainable fuel sources. Catalysis has a rich history of facilitating energy efficient, selective molecular transformations, and contributes to 90% of current chemical manufacturing processes. In a post-petroleum era, catalysis will be pivotal in overcoming the scientific and engineering barriers to economically feasible bio-fuels. This perspective highlights some recent developments in heterogeneous catalysts for the synthesis of biodiesel from renewable resources, derived from plant and aquatic oil sources. Particular attention will be paid to the importance of catalyst pore architecture, surface polarity and acid and base properties, in meeting the challenge of transforming highly polar and viscous bio-based reactants. �� 2012 The Royal Society of Chemistry.

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 ��-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 ��-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.

Optimization of Rational Approximations by Continued Fractions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials

In this paper we present F LQ, a quadratic complexity bound on the values of the positive roots of polynomials. This bound is an extension of FirstLambda, the corresponding linear complexity bound and, consequently, it is derived from Theorem 3 below. We have implemented FLQ in the Vincent-Akritas-Strzebo��ski Continued Fractions method (VAS-CF) for the isolation of real roots of polynomials and compared its behavior with that of the theoretically proven best bound, LM Q. Experimental results indicate that whereas F LQ runs on average faster (or quite faster) than LM Q, nonetheless the quality of the bounds computed by both is about the same; moreover, it was revealed that when VAS-CF is run on our benchmark polynomials using F LQ, LM Q and min(F LQ, LM Q) all three versions run equally well and, hence, it is inconclusive which one should be used in the VAS-CF method.

The Point of Continuity Property: Descriptive Complexity and Ordinal Index

��� Supported by D.G.I.C.Y.T. Project No. PB93-1142

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.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(���1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(���1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.

On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables

In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithm computing reducts of decision tables by relational database approach. Let DS = (U, C ��� {d}) be a consistent decision table, we say that A ��� C is a relative reduct of DS if A contains a reduct of DS. Let s = <C ��� {d} , F> be a relation schema on the attribute set C ��� {d}, we say that A ��� C is a relative minimal set of the attribute d if A contains a minimal set of d. Let Qd be the family of all relative reducts of DS, and Pd be the family of all relative minimal sets of the attribute d on s. We prove that the problem whether Qd ��� Pd is co-NP-complete. However, the problem whether Pd ��� Qd is in P .