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Symmetry, Volume 3, Issue 4 (December 2011), Pages 699-851

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Open AccessArticle d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry
Symmetry 2011, 3(4), 699-749; doi:10.3390/sym3040699
Received: 26 May 2011 / Revised: 8 October 2011 / Accepted: 11 October 2011 / Published: 20 October 2011
Cited by 8 | PDF Full-text (2379 KB)
Abstract
A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the
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A review of the theory describing the coexistence between d-wave superconductivity and s-wave charge-density-waves (CDWs) is presented. The CDW gapping is identified with pseudogapping observed in high-Tc oxides. According to the cuprate specificity, the analysis is carried out for the two-dimensional geometry of the Fermi surface (FS). Phase diagrams on the σ0 − α plane—here, σ0 is the ratio between the energy gaps in the parent pure CDW and superconducting states, and the quantity 2α is connected with the degree of dielectric (CDW) FS gapping—were obtained for various possible configurations of the order parameters in the momentum space. Relevant tunnel and photoemission experimental data for high-Tc oxides are compared with theoretical predictions. A brief review of the results obtained earlier for the coexistence between s-wave superconductivity and CDWs is also given. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
Open AccessArticle Symmetry in the Language of Gene Expression: A Survey of Gene Promoter Networks in Multiple Bacterial Species and Non-σ Regulons
Symmetry 2011, 3(4), 750-766; doi:10.3390/sym3040750
Received: 5 September 2011 / Revised: 8 October 2011 / Accepted: 11 November 2011 / Published: 18 November 2011
PDF Full-text (938 KB)
Abstract
The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each
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The language of gene expression displays topological symmetry. An important step during gene expression is the binding of transcriptional proteins to DNA promoters adjacent to a gene. Some proteins bind to many promoters in a genome, defining a regulon of genes wherein each promoter might vary in DNA sequence relative to the average consensus. Here we examine the linguistic organization of gene promoter networks, wherein each node in the network represents a promoter and links between nodes represent the extent of base pair-sharing. Prior work revealed a fractal nucleus in several σ-factor regulons from Escherichia coli. We extend these findings to show fractal nuclei in gene promoter networks from three bacterial species, E. coli, Bacillus subtilis, and Pseudomonas aeruginosa. We surveyed several non-σ transcription factors from these species and found that many contain a nucleus that is both visually and numerically fractal. Promoter footprint size scaled as a negative power-law with both information entropy and fractal dimension, while the latter two parameters scaled positively and linearly. The fractal dimension of the diffuse networks (dB = ~1.7) was close to that expected of a diffusion limited aggregation process, confirming prior predictions as to a possible mechanism for development of this structure. Full article
Open AccessArticle Information Theory of Networks
Symmetry 2011, 3(4), 767-779; doi:10.3390/sym3040767
Received: 26 October 2011 / Revised: 11 November 2011 / Accepted: 16 November 2011 / Published: 29 November 2011
Cited by 12 | PDF Full-text (105 KB)
Abstract The paper puts the emphasis on surveying information-theoretic network measures for analyzing the structure of networks. In order to apply the quantities interdisciplinarily, we also discuss some of their properties such as their structural interpretation and uniqueness. Full article
(This article belongs to the Special Issue Symmetry Measures on Complex Networks)
Open AccessArticle An Application of the Extended Global SO(3) × SO(3) × U(1) Symmetry of the Hubbard Model on a Square Lattice: The Spinon, η-Spinon, and c Fermion Description
Symmetry 2011, 3(4), 780-827; doi:10.3390/sym3040780
Received: 17 October 2011 / Revised: 24 November 2011 / Accepted: 30 November 2011 / Published: 12 December 2011
PDF Full-text (582 KB)
Abstract
In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically,
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In this paper we review recent results on the preliminary applications of the new-found extended global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on a bipartite lattice. Our results refer to the particular case of the bipartite square lattice. Specifically, we review a general description for such a model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N2a 1 sites consistent with its extended global symmetry. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global symmetry. Such objects emerge from a suitable electron-rotated-electron unitary transformation. An application to the spin spectrum of the parent compound La2CuO4 is shortly reviewed. Full article
(This article belongs to the Special Issue Symmetries of Electronic Order)
Open AccessArticle Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry
Symmetry 2011, 3(4), 828-851; doi:10.3390/sym3040828
Received: 4 August 2011 / Revised: 29 November 2011 / Accepted: 2 December 2011 / Published: 12 December 2011
Cited by 1 | PDF Full-text (1285 KB)
Abstract
We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are
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We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with p3m1, p4m, or p6m symmetry groups that have polyominoes or polyiamonds as fundamental domains. We display the algorithms’ output and give enumeration tables for small values of n. This expands earlier works [1,2] and is a companion to [3]. Full article

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