http://www.mdpi.com/journal/symmetry/special_issues/complexity-symmetry/ Dear Colleagues, Symmetry and complexity determine the spirit of 21st century science. The expansion of the universe, the evolution of life and the globalization of human economies and societies lead from symmetry and simplicity to complexity and diversity. The emergence of new order and structure means symmetry breaking and transition from unstable to stable states of balance. It is explained by physical, chemical, biological, and social self-organization, according to the laws of complex dynamical systems. Atomic and molecular clusters, stars and clouds, organisms and brains, economies and societies, information, computation and communication networks (e.g., WWW) are only examples of complex dynamical systems. Thus, symmetry and complexity are the basic principles of a common systems science in the 21st century, overcoming traditional boundaries between natural, cognitive, and social sciences, mathematics, humanities and philosophy. Symmetry also means unity. In physical science unified theories are explained by mathematical symmetries and invariance of fundamental laws. Are they only theoretical tools used in order to reduce the diversity of observations and measurements to some useful schemes of research or do they represent fundamental structures of reality? This has been a basic question of philosophy since Antiquity. Empirical results of modern science confirm that symmetries are not only mathematical imaginations of our mind. They dominated the universe long before mankind came into existence: in the beginning there was a dynamical symmetry expanding to the complex diversity of broken symmetries. Phase transitions involve the emergence of new phenomena on hierarchical levels of atoms, molecules, life, and mankind. They have not been determined from the beginning, but depend on changing conditions that happen more or less randomly. It is a challenge of systems science to explore their fascinating symmetry and complexity. Literature: 1. Mainzer, K. Thinking in Complexity. The Computational Dynamics of Matter, Mind, and Mankind, 5th Ed.; Springer Verlag: Berlin - Heidelberg - New York, 2007. 2. Mainzer, K. Symmetry and Complexity. The Spirit and Beauty of Nonlinear Science; World Scientific Series on Nonlinear Science Series A: Singapore, 2005. 3. Mainzer, K. Symmetry and complexity in dynamical systems. European Review , 2005, 13, Supplement 2, 29-48. 4. Mainzer, K. Complexity. European Review , 2009, 17(2), 219-452. Prof. Dr. Klaus Mainzer Guest Editor Submission All manuscripts should be submitted to symmetry@mdpi.com with a copy to the Guest Editor. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website. Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed Open Access monthly journal published by MDPI. Please visit the Instructions for Authors page before submitting a manuscript. For the first couple of issues, to be published in 2010, the Article Processing Charges (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections. http://www.mdpi.com/2073-8994/2/4/1763/ The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite  it as a partial differential equation on a fiber bundle in covariant differential form so as to have invariance in form. The paper shows the form of the pricing equation can keep invariant under all the local num´eraire transformations, this symmetry behind the pricing equation of derivatives is revealed. In addition a  corresponding relationship between the curvature of the fiber bundle and the arbitrage in finance arises. http://www.mdpi.com/2073-8994/2/4/1763/ Thu, 21 Oct 2010 00:00:00 CEST Symmetry 2010-10-21 2 4 Article 1763 1775 2073-8994 An Application of Symmetry Approach to Finance: Gauge Symmetry in Finance 2010-10-21 doi: 10.3390/sym2041763 Shipeng Zhou Liuqing Xiao http://www.mdpi.com/2073-8994/2/3/1250/ Within recent discussions in the Philosophy of Mind, the nature of conscious phenomenal states or qualia (also called ‘raw feels’ or the feel of ‘what it is like to be’) has been an important focus of interest. Proponents of Mind-Body Type-Identity theories have claimed that mental states can be reduced to neurophysiological states of the brain. Others have denied that such a reduction is possible; for them, there remains an explanatory gap. In this paper, functionalist, physicalist, epiphenomenalist, and biological models of the mind are discussed and compared. Donald Davidson’s Anomalous Monism is proposed as a unifying framework for a non-reductive theory of qualia and consciousness. Downward Causation, Emergence through Symmetry-breaking, and Dynamical Systems Theory are used to show how consciousness and qualia emerge from their neural substrate and can also be causally efficacious. http://www.mdpi.com/2073-8994/2/3/1250/ Fri, 25 Jun 2010 00:00:00 CEST Symmetry 2010-06-25 2 3 Article 1250 1269 2073-8994 Will Science and Consciousness Ever Meat? Complexity, Symmetry and Qualia 2010-06-25 doi: 10.3390/sym2031250 Roger Vergauwen http://www.mdpi.com/2073-8994/2/2/1135/ We present a review of novel techniques developed by our research group to improve quantitative assessment of human movement, especially assessments related to symmetric and asymmetric gait patterns. These new methods use motion capture data of the lower limb joints (e.g., joint and body segment angular position and/or velocity, or joint center locations) and include: (1) Regions of Deviation (ROD) analysis, (2) complexity and variability of phase portraits, and (3) multivariate shape-alignment and decomposition. We provide example demonstrations of these techniques using data from infants, typical and atypically developing children, simulated injuries of a knee or ankle, and wheelchair propulsion. http://www.mdpi.com/2073-8994/2/2/1135/ Mon, 14 Jun 2010 00:00:00 CEST Symmetry 2010-06-14 2 2 Review 1135 1155 2073-8994 A Review of New Analytic Techniques for Quantifying Symmetry in Locomotion 2010-06-14 doi: 10.3390/sym2021135 Hsiao-Wecksler Polk Rosengren Sosnoff Hong http://www.mdpi.com/2073-8994/2/1/150/ Information optimization is a centerpiece phenomenon in the universe. It develops from simplicity, then continuously breaks symmetry and cycles through instability to progress to increasingly dense nodes of complexity and diversity. Intelligence has arisen as the information optimization node with the greatest complexity. A contemporary imbalance is presented in that exponentially growing technology could be poised as a potential sole successor to human intelligence. A complex dynamical system is emerging in response, the engineering of life into technology. Numerous network elements are developing which could self-organize into the next node of symmetry, a phase transition in intelligence. http://www.mdpi.com/2073-8994/2/1/150/ Tue, 23 Feb 2010 00:00:00 CET Symmetry 2010-02-23 2 1 Article 150 183 2073-8994 Engineering Life into Technology: the Application of Complexity Theory to a Potential Phase Transition in Intelligence 2010-02-23 doi: 10.3390/sym2010150 Melanie Swan