Symmetry and Complexity - The Spirit and Beauty of Nonlinear Science

Mainzer, Klaus

doi:10.1142/9789812569400

Cited by 48 publications

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“…Namely, dissipative selforganization, emergence of new order and chaos, phase transition between chaos and/or order, and increasing returns in complexity correspond to molecular aggregation, formation of metastable phases, polymorphic transition, and substantial enrichment of one enantiomer in preferential enrichment, respectively [1][2][3].…”

Section: Figurementioning

confidence: 99%

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Chiral Symmetry Breaking Phenomenon Caused by a Phase Transition

2010

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Abstract:We report the mechanism and scope of "preferential enrichment", which is an unusual symmetry-breaking enantiomeric resolution phenomenon that is initiated by the solvent-assisted solid-to-solid transformation of a metastable polymorphic form into a thermodynamically stable one during crystallization from the supersaturated solution of certain kinds of racemic mixed crystals (i.e., solid solutions or pseudoracemates) composed of two enantiomers. The mechanism can well be interpreted in terms of a symmetrybreaking complexity phenomenon involving multistage processes that affect each other.

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Section: Figurementioning

confidence: 99%

“…In the complexity system, symmetry is easily broken by the phase transition between two chaotic or metastable states [1][2][3]. Therefore, it might be possible to observe the symmetry-breaking as a chemical complexity phenomenon by using appropriate probes such as chirality ( Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Chiral Symmetry Breaking Phenomenon Caused by a Phase Transition

2010

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“…And "the universal evolution is caused by symmetry break, generating diversity, increasing complexity and energy" [26].…”

Section: Fuzzy Symmetrymentioning

confidence: 99%

Symmetry in Complex Networks

Garrido

2011

Symmetry

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Abstract:In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features-such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.

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“…Symmetry and complexity determine the essence of nonlinear science that can describe the expansion of the Universe, the evolution of life and even the globalisation of human economies and societies [1]. As Mainzer described in his book-triad [1][2][3] symmetry and complexity are fundamental principles in science of 21 st century connecting natural, cognitive, and social sciences, mathematics, humanities, and philosophy. Symmetry was primarily related to simplicity of order, beauty and harmony.…”

Section: Symmetrymentioning

confidence: 99%

Symmetry versus Asymmetry in the Molecules of Life: Homomeric Protein Assemblies

Kojić‐Prodić

Štefanić

2010

Symmetry

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Abstract:The essay is dedicated to the relation of symmetry and asymmetry-chirality in Nature. The Introduction defines symmetry and its impact on basic definitions in science and human activities. The following section Chirality of molecules reveals breifly development of notion of chirality and its significance in living organisms and science. Homochirality is a characteristic hallmark of life and its significance is presented in the section Homochirality of Life. Proteins, important constituents of living cells performing versatile functions are chiral macromolecules composed of L-amino acids. In particular, the protein assemblies are of a great importance in functions of a cell. Therefore, they have attracted researches to examine them from different points of view. Among proteins of known three-dimensional structures about 50-80% of them exist as homomeric protein complexes. Protein monomers lack any intrinsic, underlying symmetry, i.e. enantiomorphic protein molecules involve left-handed amino acids but their asymmetry does not appear to extend to the level of quaternary structures (homomeric complexes) as observed by Chothia in 1991. In the section Homomeric assemblies we performed our analysis of very special cases of homomers revealing non-crystallographic symmetry in crystals. Homochiral proteins can crystallize only in enantiomorphic space groups. Among 230 existing space groups 65 are enantiomorphic containing limited symmetry elements that are rotation and screw-rotation axes. Any axis of rotation symmetry of a crystal lattice must be two-fold, three-fold, four-fold, or six-fold. Five-fold, seven-fold, and higher-fold rotation symmetry axes are incompatible with the symmetry under spatial displacement of the three-dimensional crystal lattice.

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Symmetry and Complexity - The Spirit and Beauty of Nonlinear Science

Cited by 48 publications

References 0 publications

Chiral Symmetry Breaking Phenomenon Caused by a Phase Transition

Chiral Symmetry Breaking Phenomenon Caused by a Phase Transition

Symmetry in Complex Networks

Symmetry versus Asymmetry in the Molecules of Life: Homomeric Protein Assemblies

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