The critical Z-invariant Ising model via dimers: the periodic case

We study a large class of critical two-dimensional Ising models namely critical Z-invariant Ising models on periodic graphs, example of which are the classical square, triangular and honeycomb lattice at the critical temperature. Fisher introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model. We prove that the dimer characteristic polynomial is equal (up to a constant) to the critical Laplacian characteristic polynomial, and defines a Harnack curve of genus 0. We prove an explicit expression for the free energy, and for the Gibbs measure obtained as weak limit of Boltzmann measures.Comment: 35 pages, 8 figure

Systems Biology Graphical Notation: Entity Relationship language Level 1

Standard graphical representations have played a crucial role in science and engineering throughout the last century. Without electrical symbolism, it is very likely that our industrial society would not have evolved at the same pace. Similarly, specialised notations such as the Feynmann notation or the process flow diagrams did a lot for the adoption of concepts in their own fields. With the advent of Systems Biology, and more recently of Synthetic Biology, the need for precise and unambiguous descriptions of biochemical interactions has become more pressing. While some ideas have been advanced over the last decade, with a few detailed proposals, no actual community standard has emerged. The Systems Biology Graphical Notation (SBGN) is a graphical representation crafted over several years by a community of biochemists, modellers and computer scientists. Three orthogonal and complementary languages have been created, the Process Descriptions, the Entity Relationships and the Activity Flows. Using these three idioms a scientist can represent any network of biochemical interactions, which can then be interpreted in an unambiguous way. The set of symbols used is limited, and the grammar quite simple, to allow its usage in textbooks and its teaching directly in high schools. The first level of the SBGN Entity Relationship language has been publicly released. Shared by the communities of biochemists, genomicians, theoreticians and computational biologists, SBGN languages will foster efficient storage, exchange and reuse of information on signalling pathways, metabolic networks and gene regulatory maps

Systems Biology Graphical Notation: Activity Flow language Level 1

Standard graphical representations have played a crucial role in science and engineering throughout the last century. Without electrical symbolism, it is very likely that our industrial society would not have evolved at the same pace. Similarly, specialized notations such as the Feynmann notation or the process flow diagrams did a lot for the adoption of concepts in their own fields. With the advent of Systems Biology, and more recently of Synthetic Biology, the need for precise and unambiguous descriptions of biochemical interactions has become more pressing. While some ideas have been advanced over the last decade, with a few detailed proposals, no actual community standard has emerged. The Systems Biology Graphical Notation (SBGN) is a graphical representation crafted over several years by a community of biochemists, modellers and computer scientists. Three orthogonal and complementary languages have been created, the Process Descriptions, the Entity Relationships and the Activity Flows. Using these three idioms a scientist can represent any network of biochemical interactions, which can then be interpreted in an unambiguous way. The set of symbols used is limited, and the grammar quite simple, to allow its usage ranging from textbooks and teaching in high schools to peer reviewed articles in scientific journals. The first level of the SBGN Activity Flow language has been publicly released. Shared by the communities of biochemists, genomic scientists, theoreticians and computational biologists, SBGN languages will foster efficient storage, exchange and reuse of information on signaling pathways, metabolic networks and gene regulatory maps

Systems Biology Graphical Notation: Entity Relationship language Level 1 (Version 1.2)

Standard graphical representations have played a crucial role in science and engineering throughout the last century. Without electrical symbolism, it is very likely that our industrial society would not have evolved at the same pace. Similarly, specialised notations such as the Feynmann notation or the process flow diagrams did a lot for the adoption of concepts in their own fields. With the advent of Systems Biology, and more recently of Synthetic Biology, the need for precise and unambiguous descriptions of biochemical interactions has become more pressing. While some ideas have been advanced over the last decade, with a few detailed proposals, no actual community standard has emerged. The Systems Biology Graphical Notation (SBGN) is a graphical representation crafted over several years by a community of biochemists, modellers and computer scientists. Three orthogonal and complementary languages have been created, the Process Descriptions, the Entity Relationships and the Activity Flows. Using these three idioms a scientist can represent any network of biochemical interactions, which can then be interpreted in an unambiguous way. The set of symbols used is limited, and the grammar quite simple, to allow its usage in textbooks and its teaching directly in high schools. The current document presents version 1.2 of the first level of the SBGN Entity Relationship language. Shared by the communities of biochemists, genomicians, theoreticians and computational biologists, SBGN languages will foster efficient storage, exchange and reuse of information on signaling pathways, metabolic networks and gene regulatory maps