Symmetry

1285 KiB

Open AccessArticle

Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry

by Hiroshi Fukuda, Chiaki Kanomata, Nobuaki Mutoh, Gisaku Nakamura and Doris Schattschneider

Symmetry 2011, 3(4), 828-851; https://doi.org/10.3390/sym3040828 - 12 Dec 2011

Cited by 6 | Viewed by 5297

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 [...] Read more.

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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582 KiB

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

by Jose M. P. Carmelo and Maria J. Sampaio

Symmetry 2011, 3(4), 780-827; https://doi.org/10.3390/sym3040780 - 12 Dec 2011

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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, [...] Read more.

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 N²_a 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)

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105 KiB

Open AccessArticle

Information Theory of Networks

by Matthias Dehmer

Symmetry 2011, 3(4), 767-779; https://doi.org/10.3390/sym3040767 - 29 Nov 2011

Cited by 27 | Viewed by 5676

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)

938 KiB

Open AccessArticle

Symmetry in the Language of Gene Expression: A Survey of Gene Promoter Networks in Multiple Bacterial Species and Non-σ Regulons

by Preston R. Aldrich, Robert K. Horsley and Stefan M. Turcic

Symmetry 2011, 3(4), 750-766; https://doi.org/10.3390/sym3040750 - 18 Nov 2011

Cited by 9 | Viewed by 4412

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 [...] Read more.

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 (d_B = ~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

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2379 KiB

Open AccessArticle

d-Wave Superconductivity and s-Wave Charge Density Waves: Coexistence between Order Parameters of Different Origin and Symmetry

by Toshikazu Ekino, Alexander M. Gabovich, Mai Suan Li, Marek Pękała, Henryk Szymczak and Alexander I. Voitenko

Symmetry 2011, 3(4), 699-749; https://doi.org/10.3390/sym3040699 - 20 Oct 2011

Cited by 21 | Viewed by 7841

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-T_c oxides. According to the cuprate specificity, the analysis is carried out for the [...] Read more.

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-T_c 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-T_c 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)

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Symmetry, Volume 3, Issue 4 (December 2011) – 5 articles , Pages 699-851

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