A double coset ansatz for integrability in AdS/CFT

We give a proof that the expected counting of strings attached to giant graviton branes in AdS_5 x S^5, as constrained by the Gauss Law, matches the dimension spanned by the expected dual operators in the gauge theory. The counting of string-brane configurations is formulated as a graph counting problem, which can be expressed as the number of points on a double coset involving permutation groups. Fourier transformation on the double coset suggests an ansatz for the diagonalization of the one-loop dilatation operator in this sector of strings attached to giant graviton branes. The ansatz agrees with and extends recent results which have found the dynamics of open string excitations of giants to be given by harmonic oscillators. We prove that it provides the conjectured diagonalization leading to harmonic oscillators.Comment: 33 pages, 3 figures; v2: references adde

Graph Rewriting for Agent Oriented Visual Modeling

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Algebraic comparison of metabolic networks, phylogenetic inference, and metabolic innovation

BACKGROUND: Comparison of metabolic networks is typically performed based on the organisms' enzyme contents. This approach disregards functional replacements as well as orthologies that are misannotated. Direct comparison of the structure of metabolic networks can circumvent these problems. RESULTS: Metabolic networks are naturally represented as directed hypergraphs in such a way that metabolites are nodes and enzyme-catalyzed reactions form (hyper)edges. The familiar operations from set algebra (union, intersection, and difference) form a natural basis for both the pairwise comparison of networks and identification of distinct metabolic features of a set of algorithms. We report here on an implementation of this approach and its application to the procaryotes. CONCLUSION: We demonstrate that metabolic networks contain valuable phylogenetic information by comparing phylogenies obtained from network comparisons with 16S RNA phylogenies. The algebraic approach to metabolic networks is suitable to study metabolic innovations in two sets of organisms, free living microbes and Pyrococci, as well as obligate intracellular pathogens

Wiener Index Calculation on the Benzenoid System: A Review Article

The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its physical and chemical properties. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to the Wiener index of benzenoid. The Wiener index values of several benzenoid compounds using cubic polynomial are also reported. The Wiener index of benzenoid supports much of the research and provides productive citations for citing the study.   Keywords: Wiener index, benzenoid, distance matrix, chemical properties, cubic polynomial, topological